This is the route I would take, you may want to use epsom salts for the soaking. Every time you soak, give the legs a gentle scrub with a soft nail or tooth brush. Hopefully that will start softening what looks like some dead tissue and slough it off.Yes those are soap bubbles he just got a scrubbing in warm soapy water and then towel dried. A few of his feathers are still a little damp. The fifth picture is of his other leg in the same area. I haven't seen any mites but they get dusted once a month, only thing is I didn't put anything on their legs, so maybe mites have been harboring in his scales, I don't know I have had chickens for years and have no idea what it is. I'm just hoping that whatever it is the vasoline, soaking , Ivermitin, and antibiotic will eventually do the trick. It looks bad enough to me that I'm surprised he can move it to stretch it. It seems to me that the black stuff is dead skin and because it is dry and scaley he finds it hard to move his leg, so maybe that is why he is constantly stretching his legs out? Not sure of any of it anymore.
I know we all do things a bit differently, but with the Ivermectin, if you have Pour On, it may be more effective if it's applied as you would normally do - to the back of the neck. I don't know how large he is, but general guidelines would be 1 drop for chicks or tiny chickens, 3 drops for bantams, 4 drops for lightweight birds, 5 drops for large birds and 6 drops for heavy weight birds. Repeat application in 14days.
The black tissue could very well be from Scaly Leg Mites or possibly injury - SLM can do a lot of damage - since this is on the upper portion of the legs, the feathers may have created a nice warm environment there for the tissue to become a little infected. I would be inclined to trim those feathers back and away from those areas - this way there is more air flow.
If you haven't done so, add some poultry vitamins to his water a couple of times a week and give extra protein (beef liver, egg, tuna, etc.) to give him a boost.
Just my thoughts.