No. And then yes.
As the professor that I am I tested this theory and the results came back negative.
It seems that Flash fire only works when it is hit by a fire move. Since no contact was made through synchronizes then no flash fire.
Interestingly, when it is bounced back via Magic bounce then flash fire does activate. Probably since it makes contact with the W.o.w and therefore activates it.
thanks to Magegon for helping with the researches