I don't think WB made him immortal. More like Kaido wanted to kill WB for some reason but WB died and Kaido is envies the fact that WB died with such glory, he was wounded to the max and still died standing in the war of the best.
Kaido is probably trying to die with similar glory which is the reason why he is trying to start another war since the main reason why he even wanted to be alive is dead and even while dying he outshined Kaido so he wants to either
1. Die because he has lived long enough and has no more reason to live since WB is dead or 2. Wants to die in glory so he starts another war.