So a couple more questions/tests - I've never had it (6000/6400/6700) do what you're getting in the video, but I'm also using a Godox TT350s which is identified as a flash via the MIS pins. That said-
does it ever do this with the flash not in the shoe? (i.e., is it a camera thing; one potential concern is if an early session with a flash that had a metal front edge that was low enough to contact/short the sony MIS pins, when the flash fires then whatever voltage was going through the center pin might ground out through the MIS and have damaged the circuitry; if this never happens when nothing is in the shoe, than this isn't likely. and assuming your trigger is fairly new, it shouldn't be pushing too much current)
does it do this when the flash is in the shoe but not turned on (maybe the flashes are sending too much voltage...)?
is your camera overheating (I've noticed the a6700 gets warm quickly, especially outdoors in the SE US).
do you have a fast card (I could hang up my a6000 by shooting fast on a uhs-1 card) - if you shoot slowly (1 shot every other second) does it still happen (you're a pro but we're grasping here)?
is everything tightened? (a loose flash shouldn't cause the camera to hang, but the sony shoe is functionally shorter than most so with a non-MIS foot it won't make as good a connection)
Otherwise I haven't run into this and I don't recall reading about it on dpr or other places. Focus/hangups have been reported with flaky lens mounts/connects but not with flash.
Good luck.
I have not tested it with the flash in the Shue but not on i will try that.
Its all tight but I can still pull it out if I pull on it its like it is never locked in the shoe.
The cards I am using are new 128 v60II Lexar cards the 1667x 250mb.
I can shoot 4k video with it and have shot a full photo job shooting all natural light photos with no flash shooting quote fast even with a girl dancing around shooting fast never a hang up. Never a problem till I started using the flash on a job but even then it did not do this right away. I shot part of the job with flash till it then messed up in the middle of the shoot.
When It first messed up we were stand-ing on the beach in one of the most humid days of the year and hot out. We shoot all our jobs on the beach. Shooting one more later today.
I have not felt it getting to hot but It dose get warm when shooting 4k video but not to much for just photos.
I think it is strange it only dose this at random with no set pattern even with the camera on a tripod and nothing moving it will end up doing this.
Last nigh I was able to shoot over 70 shots till it then messed up other times I might only get 12 or so till it messed up
I would think that if it was not going to work with a flash it would not work at all.
Also the Vivitar flash and others I showed in the photo I do not have any more so I am not using any of them I used them many years ago. I am all Godox now days.
I have two AD200 and a 360 and the manual on camera flash. I have used them on all my Nikons and a Fuji in the last 6 or 7 years. I have 4 different Godox triggers as well. One is a manual trigger with only the center pin all still have this problem after so many shots it happens.
Also at times but not always when using the flash I have seem it no longer focus at all also intermitting it will not focus at all on anything but them 10 seconds or so later it starts working agan and at times it was would not trigger the flash all the time its been very strange, But only when a trigger or flash is mounted on it and on.
I will test it with it off. Charging the battery right now