If a man becomes very wealthy, and claims he is a Born-Again Christian, but then refuses to help his best (male) friend financially, when his best friend requires specialist cancer treatment to save his life; --what would you then think of him?

Not much to be honest. If he was very wealthy and a genuine Christian then he would surely not refuse to help his friend. Christians are supposed to give to those who need their charity arent they?    What is that saying from the bible ? Is it "it is easier for a camel to go through the eye of a needle then for a rich man to make it into heaven". I believe that  this is true. I feel that most people who become rich become more materialistic and selfish and grabbing. Look at our M P s  fiddling expenses when they dont need more money. At the bankers. I hope I am wrong but it is what I have seen time and time again. Most Christains I feel are just the same.

He is not a true Christian then, nor much of a friend either.

Hmm.. That's a toughie. Because on one hand the money is his to do with as he pleases but on the other hand a good Christian should help his neighbor.
Then again, the cancer patinet could possibly get help from the hospital. Here in the Untied States EVERY hospital has to offer financial assistance - commonly called free care. Its a federal program.
So mabye the wealthy man thinks the cancer man can get help through the community.
I don't think there are any rules in the Bible that its mandatory to pay someone else's medical bills. I mean the man wouldn't be wealthy very long and the other man would still have the cancer.. And from what I understand about cancer, there are no guarantees..
I don't know... That's a tough one to answer.