What is the number of controlled burns that get out of control every
year? Controlled burns being fires set by fire departments or the
Forest service. To clarify the question further: about 7000 prescribed burns
(controlled burns) are set every year in the U.S., how many of these
get out of control?

I don't want to be too flippant with a comment to a serious question,
but it could be that the fire departments write their records after
the work has been done.  That is, a controlled burn is only one that
was kept under control; the other ones - if any, and somewhat
logically -  aren't recorded as such.
Who knows, maybe such out-of-control burns even get reported as arson.

You have a good point. I am still interested what number/percentage of
fires that are started as controlled burns (that is, started
willfully) get out of hand, that is expand beyond the originally
planned area that the prescribed fire was supposed to remain in.