Check the video amplifier/inverter circuit before you go replacing the flyback unless you have very strong reasons to suspect the flyback, as it's much easier to work on physically and the parts are much more available. The circuit for the video amplifier is the same as in the document: while I think some of the component designations are different, the actual components are the same so you should be able to follow it. This amplifier sits between pin 1 of the AB->LB cable and the brightness modulation wire heading off to the back of the CRT.
You should be able to follow the video signal through the amplifier fairly easily with a scope or similar (though be careful of course of the high voltages in the area... I solder on flying test leads and hook my scope probes onto those so I won't be probing near HV, because I am a walking disaster area). Specifically, there's a TTL NAND chip just after the connection to the logic board which I have seen cook: one of its jobs is to invert the video signal from the LB before feeding it into the video amplifier. Check the output of the NAND gate that's doing that inverting: I've had that being basically wedged low, and this will result in a black screen.
Not saying, of course, that it isn't your flyback, but there are a lot more things that can go wrong in the video section board than the flyback, many of which are easier to attempt to diagnose first.