ATK from Flitting should increase your DPS.
ASPD from Flitting should be canceled out by the fact that Overed Boost SETS your aspd to 189.
I say should, because my Eira was a Vanilmirth.
However, ASPD boosting/reducing gear/skills, either % or # based, do not effect my Genetic while under Overed Boost Status.
I'd have to assume Homunculus would be treated the same.