I will second what A.bakker already said, the only way to get her to stop being scared is to get her to play with him. Word's don't work with kids that young, they have to see for themselves that he isn't scary.
That being said the hard part is getting her to play with him that first time so she can see he is okay. I've had allot of experience getting kids to open up, but unfortunately to be really good at it one needs to know how to 'listen' to a kid (ie reading their body language and actions to understand their feelings) well enough to judge their comfort level so you know much to engage them and what is pushing to far. Still, there are a few rules of thumb I could offer Alex for getting her to open up enough to first start playing with him.
The more experience/comfort Alex has with kids in general the easier many of these will be, but unfortunately I think it's really Alex who has to show your daughter he can be trusted, there isn't that much as a father you can do without Alex.
Play with other kids around her.
The #1 most effective way to get most kids to open up, especially when the issue is fear instead of a more introverted sort of shyness, is for a child to see you playing and having fun with other peers their age. That allows the kid to see that the adult is nice with kids, and thus won't hurt them. It also makes them want to join in on the fun, giving them incentive to 'risk' playing with an adult.
If you have any other family members or friends with similar age kids having a get together where Alex is playing and getting along well with the other kids so she can see he isn't bad could help.
Get down on her level
Adults tower over kids, they are always looming and huge compared to a preschooler; it's understandable why that would be scary. One simple solution for any kid is to get down closer to their eye level when you are interacting with them. That means either kneeling down or sitting on the floor. It's a very simple thing, but adults tend to be much approachable when they are eye to eye with the kid then when standing.
Incidentally if she is being held by you that would also put her at eye level with Alex, which would have similar result of ensuring he isn't accidentally looming over her.
The title pretty much says everything. It's hard to be afraid of someone who's goofy and silly. You don't seem intimidating when your talking with a silly voice, wearing a nonsensical outfit and funny hat, and pretending to trip and fall every time you try stand up. Plus kids like silly, and the whole point is to show your daughter that Alex can be a fun person to be around rather then a scary one.
No winking or teasing
I'm sure Alex means well, but right now doing something like winking at her actually makes things worse. It's telling her "I see and am acknowledging you". Alex means it as "I see you and I'm still being nice, you can trust me" but your daughter likely takes it more as "The big scary man is saying he sees me, he's about to come get me!".
Basically you want to be careful of making her feel pressured or forced to engage with him unless it's part of an approach designed to actually get her to open up. If all he does is acknowledge her and let her run away he's just reinforcing the idea in her head that running away is the thing she should do when Alex is paying attention to her, making her more afraid of him.
Simple smiling is generally the best approach when you are interacting with them.
Force small, positive, interactions
If she is really afraid of Alex she isn't going to just switch her view immediately, so it's good to let her warm up to the idea. Instead of forcing her to suddenly spend a long time with Alex all at once instead try to focus on a few short positive interactions, just designed to show her that she interact with him and nothing hurt her. Their short so as not to push her comfort level too far, and to show that Alex will back away when she wants it. This is to get past the 'immediately running stage'.
Bringing presents could work, but only if she has to take them form Alex
Let me first say presents are not necessary if your good with the other tricks above, but if you Alex wants to try them they can work if done right. The trick is to make sure she has to interact with Alex as part of the present though. So for example you bringing her an expensive doll house and saying Alex bought it for her will likely do nothing to make her trust Alex any more, she won't connect him to the gift. Him offering her a single piece of candy if she will just come and take it from him on the other hand can work, despite the candy costing far less then the doll house.
This falls back to her getting short positive interactions with Alex. If she can get something she wants, like a piece of candy, if she is brave enough to get closer to Alex then she will likely risk it just long enough to get her candy. However, if she does that over and over again she will eventually get the idea that interacting with Alex doesn't hurt and usually comes with rewards and be willing to try it out.
This doesn't even have cost anything. Maybe he is the one that takes her the juice box she asked you for, or the cookie you already were planning to take her. Let him do the small positive things you do for her already so she can keep getting positive interactions with him.
Let dad 'protect' her as she interacts with Alex
If your daughter is actively running away form Alex this can make it hard for him to interact with her long enough for her to see that he isn't a bad guy. You need to come up with an excuse for her to interact with Alex without feeling she is being trapped by him, this is where parents can be helpful. let her 'hid' behind a parent so she feels more secure even as Alex is talking with her or trying to play with her.
Alternatively try holding her when Alex comes to talk with her, remember this brings her up to his eye level which solves another problem of making him seem less scary. This keeps her from running while letting her feel somewhat protected. Of course you don't want her to feel trapped, or as if your only holding her so Alex can interact with her. If she asks to get down to run away you should let her down for example. But usually instead of trying to get down a kid being held when timid or afraid will just sort of cower into their parent for comfort instead. If she does this that still keeps her close by Alex while letting you comfort her.
So for example holding her long enough for Alex to come offer her a piece of candy, then sending her off to play after she takes it could work to get her to have a little positive interaction with Alex.
Make running away a game
You said she would look for Alex just to run away when she saw him. This is a little different from how most kids afraid of an adult act, and could actually be used to transition her from being afraid of him to playing with him. I've actually done something similar where I had a kid who would run from me every time she saw me, but we converted it to a game where she would enjoy pretending to be afraid of me instead of out of actual fear.
For instance I might try pretending I was afraid of her, instead of the other way around. Next time she is looking for Alex give him a heads up and have him say (in an over-the-top silly voice!) something like he hopes there are no scary kids trying to find him loud enough for her to hear. Then when she actually sees him he runs from her acting afraid (but again in a clearly not serious this-is-all-a-game manner). You do this a few times and it would most likely quickly become a game to find him just so they can both run away, a sort of revere hide-and-seek.
Parents could also get in on making this a game by having one parent with her helping her to 'check' if Alex is around. Then when they find him running away with her, but in a way that makes the whole exercise more game then actual hiding in fear. For instance maybe picking her up to run with her, but then intentionally bouncing and jostling her around in a humerus way, pretending to run into a wall when turning in a hallway etc. Maybe having the parent 'hid' from Alex in a way that would clearly not work like putting just their head under the blankets of a bed and pretending their hidden etc. Once the kid has had a good laugh at the silliness the adult could suggest they go check if Alex is still there again, with the implication of repeating the silly game.
I'd call the above a more 'advanced' trick as it requires either Alex or one of the parents to be really good at over the top silliness and making the kids laugh. Some are good at that, some aren't. If your not certain you can achieve the correct level of goofiness to make it clear everything is a game then it shouldn't be tried, but if you can get it right it could probably switch the kid from fear to enjoyment of Alex visits pretty quickly by making every one an excuse to repeat a fun game.