I am not sure you could fit a 6mm Flobert into a .22 chamber, but if you can, it should not harm anything unless you get one stuck in the barrel.
My question would be "Why??". 22 Shorts are getting a little more expensive, but the last time I saw 6mm Flobert ammo it was about $30 for a box. For that price, I could buy a brick of 22 Shorts and have enough left over for sodas for the range session.