Flanagan, football general manager Darren Mooney, head trainer Mark Noakes, physiotherapist Konrad Schulz and long-serving team doctor Dave Givney were all removed from their positions at the NRL club, who are under investigation by the Australian Sports Anti-Doping Authority.
Widespread reports have suggested as many as 14 Cronulla players are under suspicion of taking banned substances.
"It is with great regret that the board has taken this course of action, but it does so given the serious nature of the management failures identified," Cronulla deputy chairman Keith Ward said.
"We make these decisions in the interest of our club going forward, in the interest of the game itself and the welfare of our playing group, which is uppermost in our minds.
"We understand that Sharks fans and all rugby league supporters will be shocked by this news, but the board determined this was the most responsible and appropriate course of action to be taken at this time."
The NRL offered its support by way of a package which included the appointment of Bruno Cullen as temporary CEO.
Cullen, a former CEO of the Brisbane Broncos, will be formally confirmed in the role pending the finalisation of terms with the Cronulla board early next week.
Former Manly and Hull coach Peter Sharp will coach Cronulla in Sunday's round one clash against the Titans at Shark Park.