For the whole Gunflame thing, generally you want it to connect towards the end, as far away as possible. The ideal range you're shooting for is f.S range. In fact, f.S is how Sol gets started. Any time f.S connects, be it blocked or hit, you should cancel it into 2S. This makes it more advantageous regardless of if the 2S connects or not. After that, you usually have a couple options. You can dash forward and FD break to see what your opponent does, or go for the f.S 2S series again. Once they're conditioned to expect that, you can try f.S into gunflame, which will net you the best frame advantage for it, and if they press buttons and it counterhits you get a combo.
In terms of hitconfirms, Sol doesn't really get the big stuff off at f.S range. At best you net the above situations meterlessly. If you want to burn 50 meter you can do f.S 5H RC bandit bringer. Ideally your goal with any hit you land is to get knockdown. Try to remind yourself that anything that connects, you want it to end in 2D. the ideal basic midscreen is 5k c.S 2D 236K, but you want to make sure anything ends in 2D. I even do stuff like 2P 2P 2P 2D if I can't quite get a good confirm. Don't sweat over doing 'perfect' or 'optimal' stuff. The goal is the get the knockdown and go from there.
Opening up people is different from the usual stuff with Sol. He lacks a good overhead so you can't go for traditional high/low like most characters. His pressure game is a grappler at heart. When you're close, the name of the game is tick throws and frame traps. 2P -> Wild Throw, 2K -> Wild Throw, etc, are all good options. After you've landed these, the opponent is gonna want to mash. That's where frame traps come in. Doing things like 2P delay 2P can net you simple counterhits, and you can simply go 2P 2K 2D, or just 2P 2P 2D afterward; it doesn't matter so long as you get that knockdown. If you're close enough, make sure you bandit revolver after 2D for extra damage and better oki set up. Other useful frame traps are 2P 6P which is extremely rewarding on counterhit; follow up with 5K 2H into the basic air combo (j.k j.s JC j.s j.H DP) and if they block 6P you can delay gatling into f.S 2S or anything else, throwing in yet another frame trap.
Antiairing: With Sol it's a little tricky. Your useful AAs of choice are 5K, DP, and 6P. Each is situational, there's no catch-all. Against jumpins with not so much priority, or if they press too late, 5K is your basic answer, going into 2H into air combo. You also have the option of running under and nailing 5K from behind.
DP is the most effective but most risky. This'll beat pretty much any jump in and if the second hit counter hits you can run up and combo off of it (picking up with run up 5K 2H -> air stuff)
6P isn't as reliable as others but has it's uses. It doesn't have as good upper invuln as most 6Ps, so you'll mostly use this against people who try to IAD or otherwise jump in at a shallow angle. On counterhit it's of course very rewarding, but even off a regular hit you can gatling into c.S 2H for a simple air combo.
You said you were struggling with the fun aspect so IDK if this is all going to be helpful to you, but I think you'd probably enjoy yourself more once you get things going. I sorta ramble a bit when I give advice so if you need something clarified just ask. And heck if he's not fun still you can always play another character.
great post.