I'd like to think through this question more thoroughly, but since I was a2a'ed, I'll go ahead and provide my first thoughts. I hope to flesh out this answer later, so consider yourself warned that this might be a bit minimalist.
My mom's fishy rule of thumb has always been, "a sick fish is a dead fish, and a fish that doesn't eat is a sick fish." She often proposes we euthanize a fish that doesn't have much appetite, and I agree that in a community tank (with lots of different fish) that sometimes it can be better to minimize disease spread than try to nurse a sick fish, but if Mr Betta is the only fish in his tank, that's a non-issue. (Using a quarantine or hospital tank is another way to make it a non-issue.) Unless a fish truly seems to be suffering, I'm reluctant to euthanize, but if you need to, put the fish in a cup of tank water and pop it in a freezer. No flushing live animals!
Bettas can actually drown if they rely solely on their gills for oxygen, so the fact that he's still alive suggests he's occasionally grabbing a breath from the surface, even if you don't see it.
The back angle is a big concern, and my gut tells me it's either genetic or from an injury, neither of which is good news for recovery. I've had fish with bad scoliosis (almost exclusively from bad breeding, mostly too much inbreeding) live long, happy lives, but they may need extra help eating. A solo fish doesn't have to outcompete tank mates for food, but he still might appreciate food dropped right in front of him, or even food "danced" around in front of him with chopsticks or tweezers. High quality frozen meats (blood worms, shrimp, and other frozen foods made for freshwater fish) are usually much more appetizing than flake foods, but can be pricey compared to said flakes.
Other things to check:
-water temp (should be 78-90°F. Keeping a betta at room temperature is lethal, although it's a slow death over weeks to months)
-ammonia, nitrate, and nitrite levels (ideally all are at zero ppm [parts per million], although bettas can handle more nitrogenous wastes than most fish, but that doesn't mean it's good for them). Most fish stores, including Petsmart/Petco, should be able to test water chemistry for free, but call to check and to be sure the sample is a good one.
-water conditioning: tap water needs to be dechlorinated and should be the same temp as the tank for water changes, and it's less stressful to the fish to change out some, not all, the water at once.
Finally, bettas live an average of around 2.5-3 years, and are usually at least a year, year-and-a-half when sold, so these fish are generally middle aged before we even bring them home. Sometimes we really don't know how to "cure" a fish, so don't beat yourself up if this fish is near his end.