I think this is a case where the alliteration totally works! I get your concern as I tend to avoid alliterative names or worry about names being too matchy, but I think the difference in length and the fact that the only shared sounds between the two names at the Fl- make them different enough that it’s catchy and memorable but not redundant.
For me, yes, it is too much. I love the name [name_u]Florence[/name_u] too, but would not use it with this surname. Growing up you hear your first and surnames said together a hundred times a week it feels - especially if you feel embarrassed about how they sound together - as I was with mine.
I would always err on the side of caution in these cases and choose some other lovely name. Your child may be one of the 90 percent who think it sounds fine, or one of the 10 percent who, like me, would be self-conscious about it. Why risk it?
[name_u]Or[/name_u], seriously, use your surname, or a combination of surnames, or a different one altogether - and keep [name_u]Florence[/name_u]!
I do find it a bit tongue-twistery unfortunately. [name_u]Florence[/name_u] [name_f]Fay[/name_f] immediately popped into my mind, so I feel like another first name that starts with F (but not Fl-) would be fine!