Well, I went out and bought this particular bracket to actually try it. It turns out that, yes, it can be used with a TLR with a WLF - the arm that holds the flash can be set forward or backward to whatever angle you want (there's a 360 degree groove on the post, and a bolt that you tighten down inside the groove to lock it in place wherever you want). Also, the flash shoe angle isn't fixed - you can also set it to whatever angle you want so that the flash points forward.
Although I already have a Stroboframe Quickflip bracket for 35mm, this VH Flip bracket may be useful for some of my other cameras. I didn't realize it uses a quick release system, though - to use it properly with other cameras I guess I have to buy some accessories
I'm with benji on this one, he actually write that he can detach it from the bracket to hand hold it. It can still be attached to the camera. I use this setup with a TLR (strangely enough the brand is called "Beauty") and a flash bracket and an old press flash. I see no need for a flipping flash bracket.
Once again, yes, I realize the flip function isn't useful with 6x6 - I was looking for *any* bracket that would position the flash on-axis to the lens, yet not interfere with the WLF - I already have an L-bracket, and if the subject is in front of a wall or solid object you get less-than-optimal shadows off to one side, even with a moderate-sized diffuser (Lumiquest mini-softbox). It just so happens this VH Flip bracket was in-stock locally, which saved me the hassle of ordering one in, and it's pretty much the same price as a new Jones J-120 with shipping.
Also, to reiterate, I like both hands on the camera, so I *don't* want to use an L-bracket as a flash holder and then remove it and hold it manually on-axis for every shot.