The hot tub is why he flares… hot water makes it worse…

Turn down the heat on the hot tub would be my suggestion. I'm OK as long as the water is under 100 degrees - Above that it's a killer! Bromides in hot tubs and Chlorine in pools doesn't bother me much, just a little. But with a new hot tub, who knows what's in your water now - could be some chemical in the new filter, a final coating put on the hot tub surface. Hot water dissolves everything! And everything is made for people with normal skin but psoriatic skin is much more sensitive.
If you ever have the chance go to a natural hot spring, especially one with sulfur water, go! Those "healing" springs really work on psoriasis. If I lived near one, I would probably have no psoriasis! (Hot Sulphur Springs CO is awesome but Blue Lagoon in Iceland offers actual medical treatments.)

Get a salt system. They’re usually in pools but you can get a converter for the hot tub. No chemicals, just add salt to the water and the filter changes it to hypochlorus acid. It’s amazing, and helps my skin more than anything else (and no harsh chemicals, doesn’t even burn your eyes)