If I was to guess from what I see, I would say the activation of the flamefist acts as doing a hit in the combo and increase the scaling like any other attack would have done, except that it does no damage, and also since most of the hits in the combo after the activation is kicks there's not much to gain from Flame Fist in the current combo. You get perhaps 1% on the last hit, but since the damage have been redused on all the hits after flamefist activation because of scaling it does less damage in total.