Flyback transformer failures aren't that common in my experience. There are specific displays where this is a common failure point due to manufacturing defects or a rough service life (e.g. arcades), but immediately blaming the flyback on any random non-working CRT you come across is way too pessimistic IMO.
A ticking sound is caused by the PSU shutting down due to overload on its output and starting back up again in an endless loop. A prime suspect is a shorted horizontal output transistor (HOT) which does not necessarily imply a bad flyback transformer - it could've blown from other issues.
You said you have experience fixing LCD monitors so you're on the right track. I'd say blow all the dust out first and have a look for cold solder joints and bloated electrolytic capacitors, sometimes you luck out and the failure is really evident. Next measure the HOT for shorts - it's normal for it to measure really low between B & E when in-circuit due to the low impedance of the horizontal drive transformer, and also some of them come with integrated low-value B-E resistors, C & E is the really important bit. When in doubt, measure it out of circuit, you shouldn't find anything more than a backwards diode junction across C-E in a good HOT. If the HOT is indeed shorted, look for bad electrolytic capacitors nearby - some techs just replace every cap on the horizontal output stage when replacing a shorted HOT, a valid shotgun approach. After that, replace it and hope for the best. 😀
