The fact that the led is on would indicate that the 20v at the power supply is Ok. Howver, could still be a connector from the power supply to J107 - 6.
Having read the schematics in some more detail I am almost convinced that the problem has to be either the LS374 or the connection to J107-6 (20V line).
Here is what we know so far:
The problem is present on all flashlamps that run off J107-6. There is confirmed continuity between J107-6 and the flashlamps, and the 20V tests OK at TP7.
Now, I have to assume that there is a separate circuit for each of the flashlamps as each can be driven individually. However, all playfield flashers (8) could fit on to one LS374 (8 flip-flops) so I guess they all use the same LS374. There are also another 5 flashers driven off the 8 driver PCB and not the power driver PCB like the other 8. These 5 are the LS, RS, Special, Totem Multiball and Jackpot Multiplier flashers. If these don't work it has to point to J107-6.
While there is continuity between J107-6 and the flashlamps, it is possible that the connection is not great (yet still showing continuity) and is causing a large enough voltage or current drop that the flashers are not being driven.
Agreed, we need to know if all the flashers bar the gun are not working. If this is the case it needs to be a problem on the 20 volt line. Connection from power supply to J107-6.