As a disclaimer, I’ve been studying Danish for a few years now, but I’m not a native speaker.
Æ is said how you would say the letter A in the English alphabet, or as A in “ache.”
Ø is like the “i” in “bird,” only a bit further back in the throat. I noticed you know some French; it might help you to know this is the Danish phonetic equivalent to the French Œ.
Å is similar to the way you would say the letter O in the English alphabet, or as in O in “old,” but without rounding off. Notice how when you say “O,” your lips close slightly as you say it, almost as if there’s a W at the end? Don’t do that.
KK is more like an English G. Ex: Lækker, “LAY-guh.”
If any Danes out there are reading this, please jump in!