This should make it pretty easy to see how union strength affects firing rates (no, I don't happen to have the data on hand). IME schools tend to avoid firing teachers even when they easily could, in favor of pushing them out, because they don't want the bad press from a firing, so my guess is firing rates for teachers are low everywhere.

We might further hope to see whether union strength affects education quality, but there are too many confounders—the states with weak teachers unions tend to be red states and to have weak economies, either or both of which may have stronger effects on educational outcomes than union activity. But, on the specific question of the effect of teachers unions on teacher firing rates, we can maybe get something like a useful experiment out of these state-by-state differences.