As far as I'm aware it does. It adds 1d6 Fire damage to its attacks. Kind of odd how it works, but the extra damage is there.
Tried hunter's mark (from the grymskull helmet) today and it didn't add any damage.
The spell summons a weapon, which then is used to perform weapon attacks.
Why do so many weapon interaction fail? And why do items like pyroquickness hat (which specify spells in their descriptions) work with flameblade?
The spell feels very inconsistent, which makes it hard to use / create a build for it.