The 3-wire flasher is shown in the schematic, but isn't really indicated that middle (green) wire actually connects to anything. It is possible that the green wire, which is a ground, only connects to to case of the flasher?? Maybe some safety idea, in case of internal shorts. Maybe this is why your flasher gets hot (but you have tried different flashers)... or you have a short in the wiring, except it would be unusual to have both sides shorted after the turn signal switch. Or an internally shorted turn signal switch.
Do you have Black, Green, and Gray wires at your flasher?
Do your turn signals flash at all, before the fuse blows?
If you disconnect the flasher and momentarily connect the black and gray together, with the turn signal switch either Right or Left, does the corresponding turn signal light, along with the cluster indicator? Or do you get a BIG spark, and no light(s)?
These circuits are rather simple and a 2-wire flasher should be just as usable. The cluster indicator is wired between the two feeds to the right and left lights. Whichever turn signal bulb (side) isn't lit serves as the ground for the indicator.
It is probably best to isolate and test each turn signal light individually, to verify that they function. By unplugging circuits, checking continuity, and also checking for shorts, you should be able to pinpoint the problem.
You do have a multimeter, I assume... yes/no?
What types of flashers are you trying? Part numbers?
Check this page and see if any of the flashers are what you have:
http://autolumination.com/equalizers.htmIs your flasher P X L or P + L?
Sounds like you may have an electro-mechanical type flasher and not sure if it would work on 6-volt.
Seem to be variations for either LED or incandesent lighting also.
Wish I was there to help, as remote troubleshooting always has it's difficulties.
I keep re-reading your issue.
Does the flasher start flashing/clicking as soon as you connect it, even with the turn signal switch centered?
I suspect a short circuit before the turn signal switch or in the switch itself.