I think you can talk to your child at any time, keeping in mind that it may be distraction, especially when it is time to go to sleep.
During breast-feeding, the child will be focussed on feeding, and will generally be in a quite relaxed state. Talking gently during this time is likely to be good for the bond with the child, but it could also be distracting.
Story-time should allow the child to completely focus on the story, partly to calm the child down, but also to build the tradition and love for books. Mixing this time with feeding could create the wrong associations. It is also unnecessary to do so.
That said, child-raising is a very delicate business, and the only truly universal rule of parenting at this stage is "Do whatever works for you."
The correct time for story telling varies from child to child and as the child gets older. Initially, anytime is good time, as long as it doesn't disturb the child. In those days you can even get all the way through the story. If the child starts to love story telling, then you may find yourself reading the same story 10 or so times per day. They may not understand a word, but it is useful for their development, and of course building a parental bond. As the child gets older, the time and the way of story telling will change.
At present without our 16 month year old, we read sometimes when she goes to bed, unless she's too tired. Sometimes it will be one story, sometimes three. We also read a couple of times during the day, but only if she is a bit tired. These days we never read all the words, as she doesn't have the patients for that. We just describe the pictures. But we are already witnessing a change – she is starting to want to hear more of the actual story.