If I can't do any flips on the trampoline, I'm not sure it's worth it.

I don't have any statistics handy, but once you learn flips from an instructor and practice about 1000 times carefully and under supervision over several sessions, it is a safe activity, because of the muscle memory taking over. Unless you make it unsafe by pushing your limits or jumping while impaired. Of course, there are always freak accidents like this, but the odds are at the noise level, such as being rear-ended hard when driving.