Have Flotex in the kitchen and love it, didn't know it would work on stairs.
It sure does. The only difference from carpet is that each step is cut individually as it doesn't like the sharp bend at the back of each step but it's fine with the gradual bend on the nose of each step.
We had it fitted by a Flotex approved fitter and I'd certainly recommend that as he really knew what he was doing with it.
Our last lot of Flotex in the kitchen was down for 15+ years and, apart from normal cleaning, we lifted it every couple of years, took it out onto the patio and used a power washer on it ! !
Bob.