It's a definite no from me.
The only exception to that would be if she had said something that made it clear she was starting to think romantically of you, and things had warmed between you. In those circumstances it might be a nice thing to do.
But as it is, there's nothing to tell you she is feeling that way. You've noticed that things are better between you, but for some people, once the pressure of being unhappily married / having the separation conversations is over, they are able to be more friendly with their ex. It doesn't mean they want to get back together.
If you think there is a chance that she'd like to rekindle your relationship, then talk to her, ask her if that's what she's thinking. If she says yes - then buy the flowers if you think she would like them.
If you just buy the flowers without knowing her feelings, it could backfire. It could be awkward. She could think you've 'forgotten' you're separated and it could take your new more amicable relationship back a few steps.
Not everyone likes to receive flowers. And for those who do, context is everything. My Ex-DH used to buy them whenever he'd fallen off the wagon (again) and so they just irritated me. It seemed he felt I was so shallow that a bunch of flowers would make me forget all the bad stuff.