How to help my cat with a painful knee injury and luxating patella?

I hate to hear that about Blaire. I am concerned that you mention extreme pain. While cruciate ligament tears are painful, most cats limp and are somewhat uncomfortable but are generally not described as being in extreme pain. I do not have any more information about Blaire so I will discuss some general things.
Things that do cause extreme pain are blood clots blocking the blood flow to one or multiple legs. A urethral blockage will also cause extreme pain. Both of these conditions are emergencies and can be fatal if left untreated. That being said, other things can cause extreme pain as well. Each pet also has varying degrees of pain tolerance and some are more stoic thank others.
If Blaire is really uncomfortable, I would recommend to have Blaire examined by a veterinarian asap to make sure there is nothing more sinister happening. Cats do not tolerate human pain medications so there’s nothing safe over the counter to give him that would be effective. The veterinarian may be able to give Blaine pain killers to make him hurt less and that are less likely to damage his organs.
For a knee injury in general, gentle massage, a cool compress (not too cold) and keep Blaine from walking around or jumping tend to make them feel better. Omega 3 Fatty acid supplements also help to naturally decrease inflammation and they could help as well.
I do hope this helps and I hope he feels better quickly!