"Advance knowledge" usually means "knowledge before something happens".
For example: "If you have advance knowledge of a crime, then you should tell the police so that they can prevent it."
So in that case, the meaning is quite different from "[a] high degree [of] knowledge".
It is also possible to use the "advance" in "advance knowledge" is a verb meaning "increase".
For example: "If you want to advance knowledge, then you need a PhD."
So in that case the meaning is also different.
If you want to use a phrase with the same meaning as "a high degree of knowledge", then you should write "advanced knowledge" (note the "d").