— Adam Schefter (@AdamSchefter) March 5, 2012
The deadline has passed, NFL teams may no longer use the franchise tag, and the Green Bay Packers did not use it on Flynn. He'll be an unrestricted free agent looking for a new team.
No one is exactly sure how the NFL determines compensatory draft picks, though Mocking The Draft expects the Packers will receive four of them this year (3rd for Cullen Jenkins, 4th for Daryn Colledge, 7th for Brandon Jackson, and a 7th for Jason Spitz), but Kevin Seifert said "Flynn's exit should net the Packers a third-round compensatory pick in 2012."
That's not as valuable as a 2nd round pick this year, the compensatory picks are always at the end of each round and a year delayed means it will take an extra year to develop that player, but the Packers are still getting something good for a player they could have never afforded to keep.