Generally speaking to deal with Sol's specials you stuff them before they're out as opposed to punishing on block. I will say Sol's Bandit Revolver (the kneebash hop kick flip kick thing) can be punished by a throw if he does it too close, especially if he happens to do it after a dash.
Fafnir can get blown up by anything that happens to low profile. I think at some point you mentioned you play Ky? His Sweep, his crouch Slash, and his stand Slash can all stuff Fafnir if you get a read on what ranges a Sol wants to use it. Alternatively, instant blocking it leaves him slightly minus so you have a bit more free reign to press buttons afterward.
Bandit Bringer (the jumping flame punch) can be stuffed by reading/reacting to it and doing rising j.Ps or j.Ks. Or just straight up DPing it.
Riot Stomp is a pretty obvious one. Pretty much the whole cast's 6P will blow it up. Ky's 2HS is pretty amazing for that as well.
For Gunflame, it depends how far away he is. it shoots 4 pillars in a row. If the 3rd or 4th pillar of fire is the one you happen to block, he's probably neutral or plus. If you happen to block it really close you usually have initiative.