I think you are confusing him with former Flyers prospect Roman Malek. He was the one who thought he had a ton of leverage to make demands in an NHL offer, and ended up missing his window of opportunity on an NHL career.
Kovar never said anything about not wanting to play in the AHL; as a young unproven goalie (until the last couple years) he wasn't in position to make any demands. He was a disappointment in Canadian Jnrs and Czech junior national team, went back home to Extraliga (which has been a mediocre league in recent years), and served an apprenticeship as a backup to Roman Turek. Eventually he became the starter and has become of the top goalies in that league.
No teams in KHL, much less the Flyers or other NHL teams, have been beating Kovar's door to sign him. He's extended his contract with Ceske Budejovice a couple times.