Ball flight, yes. Distance, not necessarily. You will gain distance if you change to a proper flex from an improper flex usually, but otherwise you likely won't unless your spin/launch are way out of whack.
If you're launching it too high, then you could look into a higher kick point shaft such as the C-Taper or get something hard stepped/half a flex stronger.
If it balloons in the air, then you also would want to get a lower spinning shaft, which would increase distance in that case.
Also depends on ball speed. For a lot of slower swings, spin rate will keep the ball in the air longer so they can maximize carry, for irons that is important. so there is a balance there.
For irons i am not sure if kick point matters that much. Look at Adam Scott, he uses a driver with a mid kick point. I think as long as you nail the spin rate to your swing speed, then kick point is just preference. I am not sure the kick point launches the ball to higher or to lower.
Maybe i will find a demo day coming up, and go hit the same iron with three different golf shaft, see if i can tell the difference. Though having a trackman would be nicer. I wish someone would put together a conclusive golf shaft list based on swing speed, giving actual numbers to launch angle and spin rates.
Cause i always wondered, what kick point will do is change the dynamic loft. Basically increase it, not sure by how much. But this means at least for a driver, a lower kick point should increase spin and launch angle. Though i wonder how it effects angle of attack as well. If you have a lower kick point wouldn't that increase angle of attack for the same swing?