Asked if he felt he was about to get the sack, Flynn replied: “I hope not, because I really love this club and enjoy working here.
“But it is a results business and I’m not stupid. I’m someone that is going to come out here and speak open and honest, whether that is good or bad. And things have to improve.
“And if I still am [in charge] they have to improve quick.”
New owner Mike Garlick completed his takeover of the club on 23 August and had appeared to back the Welshman, saying Flynn was “the man” to turn the results around despite a run of five straight league defeats at the time.
Yet with one win in the four League Two matches that have followed, Garlick has decided to make a change.
Cheltenham are now looking for their fourth manager since 2022, following Wade Elliott, Darrell Clarke and now Flynn.