Flame Blade is a scimitar, but it's not a standard weapon. It uses casting stats instead of STR and thus Finesse doesn't make much sense (Since it's still based on casting stats not martial skill)
That said, if some Rogue build wants to, they can still utilize it. Given the lack of stat requirements for a typical Rogue (I.e. Dex and Con) leaves you with options for pumping a 3rd stat to enable use of Flame Blade - Such as WIS if you're dipping Druid or CHR if you're a Tiefling.
In regards to Pyroquickness Hat, I've seen mentioned that it's not just about dealing fire damage twice, but rather bugging out when using certain bonus actions such as a Quickened Spell or an off-hand attack. Either way, a fix would be good.