I say be careful! I've done fwb twice and both times it was kind of an emotional minefield.
The first time, we'd broken up, and she wanted to get back together. I didn't, and just enjoyed the "free sex". If she'd given me something for my birthday, it would have been weird at best and awkward if she'd given me something nice or expensive.
My other fwb experience was the reverse: I wanted to get back together; she just wanted the sex. If she'd given me something for my birthday, no matter how small, I'd have read way more into it than I should've.
But if neither of you is hoping for more from the relationship, then I THINK a gift wouldn't be a problem. Something sexy seems appropriate, and nothing too expensive. Maybe some sexy undies?