I'm going to flake on a birthday party
Why do you plan to ditch the birthday party?
I usually go to her parties but this time, I'm don't know what to give her
People expect their friends to be reliable and there from them. Your friend's birthday is important to them, and it's better to go without a present, or even with a bad one, than to not go at all.
What if I say I don't have time?
I don't think you should do that, because it would be dishonest. I think it would be better if you went to her party, because that's what you said you would do. It's impolite to say you're going to do something but then not do it.