I don't believe sending the flowers was a mistake. Your female friend said she didn't think it was either. Gucci and others can disagree with me (and your friend) and that's OK.
I don't think it set you back, and even if it did it's a small thing.
I would not e-mail your wife and tell her you're sorry for sending them. To make a little joke out of it to you, that would be "double pursuing". I would just drop it. It was a birthday gift to your W for goodness sakes. Just don't go overboard. Overboard is manipulative.
One of Greek's posts helped me to realize what may be accurate in my situation. Since Greek was a WAW who came back, I value that input. What I have noticed in the course of several weeks is that my W shows some indecision and doubts when we need to do more stuff with paperwork (legal/financial). Of course the divorce process is different depending on where you are. But now that I think about it, some of our most productive discussions came when we had additional paperwork to do.