The whole wooing with OTT gifts seems sweet and traditional but it's also a sham, as you would have to keep doing it or raise the bar each time to avoid disappointment. If you do get anything, it would be a 'reunion' sort of thing, and something modest but sweet like a bracelet or chocolates. Nobody gets first date presents, if you want her parents to like you, just wave up to them, be sincere. You can also offer to pay the bill and get her an extra dessert, that could be your 'gift'.
The flowers are sweet but corny for a first date since you don't know how it's gonna go. I'd save it for your first anniversary if it does go well.