Flynn has joined Darlington for a month while Denton and Eastwood have moved to Blue Square Premier League side Woking.
Beckett told the club's official website: "It's a good move for the club and a good move for me. I've been a bit disgruntled with the situation for a while and I've been trying to get away on loan, but nothing's really come up.
"I actually spoke to Gerry Murphy when he took over from Andy Ritchie at the end of last season, but I decided to give it one more year in football.
"Stan Ternent then came in and tried to sort out a move to Bradford City for me, but I think they always wanted Michael Boulding as first choice. I've had two-and-a-half happy years here, but my football has been up and down."
Beckett scored 33 goals in 96 first-team appearances for the Yorkshire side.