OK, so what I am reading is... her "normal" behaviour is pleasant... but you HAVE witnessed a nasty side to her. Take note of this reality.
The two of you were M less than a year ago, how long did the two of you date? How long have you actually known her in any significant way, other than or prior to "she caught your eye and you sent her flowers".
I want to be very clear with you right now. If you hope to get back together and possibly start a new R and eventually re-M, I fully support you.
That said, I think there's a lot that you don't know about your X and while you might be willing to take the bad with the good (that's what M is all about, right?).
Understand that underlying, "normally" hidden nasty side of her, which appears to come along with passive-aggressive behaviours, should be a clear flag for you. Not to discourage you, but to be sure you understand what your are dealing with. If you have just M'd and D'd someone in less than a year, this person may have a DSM-V (ie. personality disorder) condition that you, and even she, may not be aware of.
Regarding her b-day, it WOULD NOT BE APPROPRIATE to send her flowers or a card or wish her happy b-day...
Until you can be 100% honest with yourself...
That honesty MUST be... you would not be recognizing her b-day with any intention to get back together with her.
