After the stroke, he could have some neurological issues and the signaling can be interrupted to the bladder. This then causes issues with the ureters and kidney and bladder and can lead to leaking. Also, has he had his prostate checked? A larger than usual prostate can cause leaking and the larger prostate could be caused by cancer obviously but also from benign prostatic hyperplasia. MS can cause it, alzheimers and parkinsons. But that he simply had a stroke is enough. It's not uncommon, unfortunately, post stroke.
If you have him evaluated to make sure there isn't a medical reason besides that he has had a stroke, then ya, do what you can to help control it. I'd ask his urologist for recommendations. Even physical therapy with someone that specializes in this would be excellent. (incontinence is a relatively common issue and PT's can be trained to work specifically on pelvic floor muscles). Is your idea behind the anti inflammatory because if he is prostate is enlarge, that will reduce it? There are also other medications to try besides the one he is on and various other treatments including surgery.