AvatarNathan Richer

Thanks for the comments!

Which flossing one do you do? The standing one where you distract back and bend over, or the one that i described where you’re laying down and lifting/flossing one leg, with band distraction? If one doesn’t work, try the other. For me, the standing one didn’t do anything for my condition, but the one laying down works much better.  That’s not to say one is better than the other overall; it just means that for a given condition, some things work better than others. 
Without looking at pics or videos, I would say that the DL may have started the problem, resulting in some ham strain. But what you describe seems more spinal than muscular, meaning that your posture while sitting is not optimal and that may be causing a disc to bulge out and touch nerves that shoot the burning sensation down your leg. It may have been non-optimal posture while doing DLs that started you down this path. I know you think it’s not nerves, but what you describe sounds like it is, especially since you say that your sitting posture is not optimal, and when you stand up and walk it goes away.
You may want to find someone to doublecheck your spine – can you get an MRI done? that would be conclusive. 
other than that, when you sit, you shouldn’t be leaning back. you should be finding a neutral place where you feel that your spine bones are stacked on each other and there shouldn’t be any extra tension anywhere holding you upright.  this takes practice and some exploration on where your optimal posture should be. for reference, optimal posture generally means you should have your ear hole line up with middle of shoulder, line up with elbow, line up with middle of hip (and if you’re standing, continue that down to the knee, and then ankle bone). you can have someone take a side pic of you sitting. are these lining up?
if not, then you will want to address those points from hips up to head. it could be forward head on neck, shoulders that are biased forward in their sockets, t-spine posture not right – either curved forward or back, lumbar spine arched forward or over extended back, pelvis positioning – it should be neutral and not have any tilt too much to the back or front.
you may consider a wedge that tilts your pelvis forward – that may relieve some of the pressure and help with the ham soreness. I cannot speak for that chair you posted, but the best chair i have found is this one: http://gokhalemethod.com/chair.