Pets

You can paradoxically build trust with cats by making a point of ignoring them. When they're around you just calmly meet their gaze for a second so they know you're aware of them, then turn back to whatever you were doing. With people or dogs this might be disrespectful but cats interpret it as a gesture of non-threatening-ness, you're announcing to them that you're aware of them and comfortable with them being around doing their thing.

If he approaches you on his own, you might just meet his gaze again, turn a little bit away again and set your hand down next to you where he can reach it if he wants. It's slow going and he probably won't ever completely shake old habits, but knowing how to "talk to" cats is important and not always intuitive.

It might not be a thing that will ever change. It won't be that you didn't do a great job being a cat parent though.

You could try mood altering medications. Probably check with a vet to see what your options are. (Maybe there's some decent research on how CBD affects cats, something that won't require a prescription and might be easier to get something that can be mixed into food or water).

Anectdote: Spouse brought home a kitten (like barely weaned) that was freaking out at a farmer's market in a local big city. We had her for something like twelve years. She was standoffish around us for something like eight years then suddenly turned into a cuddle buddy. Never was okay with anybody but us though. If there were strangers around she'd make herself scarce until they had left.

Are there any foods he absolutely loves? My greyhound was similar when I got him but I built trust by throwing a piece of cheese or sausage near him a couple of times a day until he got used to me as a snack dispenser, then serving the snacks from my hand and giving him one or two light, brief strokes, and slowly built up over a year or two until he loves cuddling now.

edit: also, this bit

but he seems conflicted. He'll purr, but also flinch in terror, then eventually bolt away.

probably won't ever completely go away. It's a trauma reaction (mine's a former racer, so you can imagine what types he'll have) and even if they manage to mostly overcome it there will be times where it bubbles back to the surface. My grey still can't stand to have his belly touched, even though we've had him nearly 5 years now.

we had a dog that we adopted at about 3 months old. she lived with us for 15 years and was always a perfectly happy, healthy, energetic, friendly dog that loved everyone. she never stopped flinching when anyone tried to touch her face. in three months someone had managed to traumatise her in a way that lasted for the rest of her life, and she didn't even have any injuries. even in the best possible circumstances some things like this will never be able to be undone, and comrade, you are helping an animal from practically the worst possible circumstances.

he might well be flinching his entire life. all you can do is listen to him and interact with him in the ways he'll allow. the fact that an animal with that background even lets you be near him is massive. he loves you, he just can't express it in the way most cats would.