- Canon Speedlite 430EX II
- Canon Speedlite 430EX III-RT
- a pair of Yongnuo YN-622C
- a pair of Kaiser Multi Trig AS 5.1
- Sony a7R II
You can't do it without additional gear.
To do off-camera flash with two flashes you need:
- a master unit (radio transmitter or master flash) on the camera
- a slave unit (radio receiver or optical slave) on each flash
The Kaiser triggers and the Yongnuo YN-622 triggers are incompatible with each other, so you basically only have two transceivers (YN-622s) or two receivers (Kaiser). And you kind of need three units: one for each flash and one for the camera.
If your flashes had optical slave modes in them that the Sony α7R II could "speak", you could go that route, but Canon's 430EX units only understand Canon's wireless eTTL system, not the one that Sony uses, and have no "dumb" optical slave modes, like Nikon's SU-4 mode, or S1/S2 modes on a lot of cheap 3rd-party flashes. And your α7R II doesn't have a pop-up flash, so you'd still have to buy a flash to go on the hotshoe.
Also, since all your Yongnuo gear is Canon-flavor, and you're using a Sony camera, you can only achieve manual triggering; no TTL, no HSS, no remote power control. If you had a YN-622-TX [for Canon], you could probably at least regain remote power/zoom control through the YN-622C, if they were used as receivers on the feet of the 430EX flashes, but that's about all (I use that combo on my Panasonic GX-7 and X100T with my Canon/Yongnuo eTTL flashes).
The only thing that you could do, if you didn't want to purchase additional triggers, would be use one 622C on-camera as your transmitter, and then split the sync signal from the other 622C (as a receiver) with a y-cable to both the flashes. But since none of the 430EXs have sync connectors, you'd have to also purchase flash foot-to-sync adapters.
Honestly, at the time of this writing, I think you're better off selling everything and just getting a pair of Godox TT685-S or TT600-S speedlights (both of which have Godox X transceivers built-in, so you don't need add-on triggers) and an X1T-S transmitter. That way you'd have gear with the Sony MI hotshoe/foot, HSS, and remote power/zoom control. The TT685 is TTL capable, the TT660 is manual-only. Of course, all this could change in a few months, with the rate that Chinese gear innovation spins. (See also: flash havoc's overview of the Godox X system).