Great question -
I have been disappointed as the years have passed that Tamiya/MM have not put out a tire black. Gunze makes a flat tire black H077 which I believe ends up looking more 'sticky' than flat black; has more surface texture when dry. That being said I think the best tire black out there is from Polly Scale. I believe using a tire black color instead of flat black gives it a more realistic foundation for weathering them later.
One can make a dusty brown/very slightly steel (from the tracks) mixture (to your preference) and dry brush the outer edge of the wheel, the part that comes into contact with the track. Brown pastel chalks in a very fune dust work well there. You're going for a look of highly impacted, fine ground and coated dirt and dust, not neccessarily rust or oily residue. The profile edges can be weathered/aged along with the with the rest of the wheels. Washes (like artists oils in MS or turpenoid) are almost essential here, and I cover the entire profine of the wheel/tire, but not the leading edge, with this. The profile is where you may try to highlight a more accumulated, oily, muddy, or even chipped look. I usually do not 'chip' the rubber, but do so with the rim of course. The concave pocket of the wheel face would have been a wonderful accumulation zone for dirt and grime that would be worn very fine/ground down on the leading edge of the tire.
Mud treatment will of course cover it all and would be an alternative to this. There are lots of cool ideas for mud simulation at this forum.