You heard a "zapping sound" and assumed it was the flyback.
While that is certainly possible, I can tell you that from my years of experience servicing CRT video, on a purely percentage basis, it's more likely the the horizontal drive transistor that is the culprit.
So, open it up and:
1) Examine the flyback. If it has an obvious burn or crack, well duh, it will need replacement. But even if it looks/is bad…
2) Test that transistor with a multimeter. Both terminals and the case, all combinations in both directions. You're looking primarily for a dead short, so you may not have to even remove it to test, but do so if the results are at all uncertain.
The transistor or its equivalent can be easily found… the flyback, not so much. It IS possible that both are bad, but if you can't see a crack (even hair-thin) on the flyback the odds are in your favor it's just the transistor.
Don't forget, since you didn't actually see it happen, it's possible that neither of them are bad. It could be something else entirely.
Fun, huh?