Does the Osmos Mobile work with the Samsung S6 Active and if so, does 4k video work?

I don't think that there is any problems with your Samsung S6 Active, its a s6 in a rough case. But better ask DJI support.

To the 4K. Your camera has UHD 4K (3840 x 2160) @30fps so here you should be fine.

jetforce Posted at 2016-12-16 02:55
I don't think that there is any problems with your Samsung S6 Active, its a s6 in a rough case. But better ask DJI support.

To the 4K. Your camera has UHD 4K (3840 x 2160) @30fps so here you should be fine.

Thanks for the info. I know the camera has 4k but I keep seeing people saying that 4k video doesn't work with the osmo mobile.

There was a DJI GO app 4K issue back in September, but it was fixed. On my galaxy s7 it works. I have a s6 somewhere, I will test it later on, and let you know.

In my experience, the DJI GO app and Osmo Mobile don't support 4K or Active Track(AT) with Android phones (you can get AT to work if you use an old 3.0.0 version of the app)  You can record 4K with your native camera app.  I do most of my front camera work with the default Samsung camera app, and use the rear camera with the 3.0.0 version of the DJI Go app, so I can get Active track at 1080P.  It sucks, but that seems to be the state of things at the moment.
*Note.  I just noticed you're asking about the the phone being supported, and not the app.