I was watching indepth on cspan booktv with Michio Kaku and he says that the Planck time has not be proven. I thought it was a proven fact, but he says it is still theoretical and we have no evidence for it yet. Is this true?
The way you put it that doesn't really make a lot of sense. Planck time is defined as the time associated with the Planck length, which is defined as a length scale where we know that QFT comes in conflict with GR. That's simply because at this length scale energy would be so concentrated that it becomes very relevant for space-time geometry as described by GR. So there's nothing to "prove" about Planck scale.
What you might be referring to is an actual theory that does work at planck scale. There are candidates (basically the usual theories dealing with quantum gravity), but there has not been enough experimental evidence or theoretical prediction to decide which of the ideas describes nature best.
But do we have evidence for QFT or is it just a mathematical model at this point? For example, I'm pretty sure we have evidence for the Planck constant in the equation, E = hv, but do we have evidence for the Planck time and the Planck length?
It's one of the natural units based on the universal constants. If anything it is a defined number. We don't know if they have any inherent value-it will depend on future theories and experiments-but they are the units derived from h, c, and G.
Planck time I believe is the time it takes a photon travelling at c to cross one Planck length.