The triple move comes as somewhat of a surprise, especially regarding striker Strevens, who has made 15 appearances over the first half of this season.
Young defender Essam was also thought to have a strong future at Priestfield while goalkeeper Flitney has recently returned following a lengthy spell on the sidelines due to injury.
Manager Martin Allen told the club's official website: "Ben Strevens is a very important member of our squad. He has a great attitude but finding him a place in the team and on the bench has proven to be difficult.
"He will still be involved with us but I've promised that if clubs come in for him, to give him an opportunity to play and maybe earn himself a new contract, then we will not stand in his way. Ben is in our squad for Saturday's game at Bristol Rovers."
Allen added: "Connor Essam will be made available on a free transfer to give him a good opportunity to find a club as he is a good young player. The club will retain an interest by including a percentage sell-on as I still feel Connor will have a good career."
Meanwhile, midfielder Bradley Dack has joined Blue Square Bet Premier side Braintree on a one-month loan deal.
Young quartet Jack Evans, Alex Brown, Tom Brunt and George Humber have also been released by Gillingham.