I'd discuss this with your parents and then follow their lead. Props to you for stepping up to the plate and taking responsibility, but I don't think its actually your problem. All young children encounter scary stuff from time to time, and often will latch on to one particular thing as a focus for more generalised fear of darkness or strangeness. So its actually a routine childhood thing, and its not your fault that he happened to latch on to something you showed him, rather than something he read or saw on the TV.
For me it was the Daleks, and I also went through a phase of being convinced that any unexplained ticking noise might be an IRA time bomb.
Edit: in response to @personjerry's request for more info:
I can't give you a recipe, but here are some pointers for talking to him about it:
Acknowledge his fear as real and valid. Obviously "Flowey" isn't real, but your brother's fear is. Telling him he is being silly or childish won't deal with the fear, but it will stop you from helping him. Talk about times you felt scared. Try to establish understanding based on common experience.
Something that Terry Pratchett wrote (from memory, so it may not be word perfect): "Fairy stories don't tell children there are monsters. Children already know there are monsters. Fairy stories tell children that monsters can be killed". Does Flowey meet a bad end? Can you arrange for your brother to play that part of the game and win? Its only a guess, but maybe conquering Flowey himself would be part of the solution. After all, if Flowey is there in the dark, logically the weapons to defeat Flowey would also be there, since they are part of the same universe.
Does your brother watch/read any heroic fiction (IronMan/Batman/Superman/whatever)? Could he imagine having his favorite hero standing guard?
A standard technique for dealing with phobic situations is desensitisation: suggest to him that he practice being alone in a dark place for a short limited time, like in a dark cupboard for a minute, with you standing outside to tell him when the minute is up. Then get him to extend it. Don't force this; you need him to agree to stretch himself, but not to the point of being distressed. If the idea upsets him then back off.