Hi, McDesign25:
No, "FLEX" feature will not distort a triangle or diamond shape into round.
If you create a spring with triangle or diamond wire (make sure one of corners coincides with your helix), it will create an edge equivalent to your helix. So, when you apply a "FLEX" feature, it will bent this edge (a helix)into a new edge that you can use as a sweep path to create your new bent spring. Of course, you need to create a new sketch with a small circle (your round wire) to do your sweep. The trick here is that "FLEX" can not bent a helix curve, but it can bent edges/bodies.
So, you will get two bent spring bodies. The first body is a bent spring with a triangle or diamond shape wire. The second is the bent spring you want. You just need to suppress the first one.
Good Luck!
Alex