I would want to know what's causing the cat's throat to be inflamed first before trying anything. Could the kitty have eaten something irritating or toxic? Does it possibly have stomatitis? Does the cat have bad breath? Is he eating okay? Any drooling, vomiting, lip-licking?
What about a vet visit?
In the meantime, slippery elm bark syrup can be soothing to mucus membranes, but it really would be a good idea to figure out the cause first.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler