Flanagan lost his starting job to Steve McKinney in training camp, but started the last 13 games after McKinney suffered a season-ending injury. The 12-year veteran started 22 games in his two seasons with the Texans.
Barber had two tackles in six games and spent the last eight games of the season on injured reserve with a neck injury.
Putzier spent two seasons with the team and had six catches for 39 yards and a touchdown last season.
Hodgdon spent four weeks on Houston's active roster and played in two games last season.