I'm trying to say that someone agrees to fly to Europe, is it correct to put it that way?
"To be good with (something)" is very colloquial for "to find (something) acceptable or satisfactory", "to be satisfied with (something)". I think it's a fairly recent idiom, and I don't know how broadly used it is; I'm in the U.S. It's used correctly in your sentence, as long as such casual language is appropriate for the context.
So, "He is good with flying to Europe" means essentially that flying to Europe is fine with him.
Also: "Would you like another drink, sir?" "No, thanks, I'm good," meaning one is satisfied, has had one's fill.
"He's flying to Europe" "He's good flying to Europe." "He's with flying to Europe." "He's good with Europe."
In the end, it's kind of like responding to the quesion "Do you want more salad?" with "I'm good!"
You aren't really good, and even if you were, you could possibly eat more salad and not become bad. It is taken to mean, however, that you are in a state of contentment without more salad. It's bad English, but people understand it.
I would say "He is happy to fly to Europe."