"I've watched John play in Blackburn reserves and he's impressed me," boss John Coleman told BBC Radio Lancashire.
"He's a good lad and wants to work and learn and he'll be a big bonus as we haven't got a great deal of cover."
Flynn is unavailable for Accrington's FA Cup Second Round tie against Barnet on Saturday because he is cup-tied.
Sydney-born Bouzanis, 19, who has Greek parents, helped Liverpool reach last season's FA Youth Cup Final against Manchester City.
Once we pay off the money we owe to the PFA it'll be business as normal Accrington manager John Coleman He has represented Australia at Under-17, 20 and 23 levels as well as making three appearances for the Greece Under-19 side.
"He's very highly regarded," said Coleman. "He was due to go on loan to Wrexham last year but couldn't go because he was called up for the Australian squad.
"He's another who's keen to play as he doesn't get a lot of games in the reserves because Liverpool have a number of keepers.
"I want people with that attitude. They're not just content to sit and train with Liverpool week in, week out with no game at the end of it."
Coleman has been able to add to his squad after one of the club's transfer embargoes was lifted.
But despite repaying £80,000 to HM Revenue and Customs they are still limited to a maximum squad of 20 players.
The remaining embargo will be lifted once an outstanding £55,000 debt is repaid to the Professional Footballers' Association.
"Once we pay off the money we owe to the PFA it'll be business as normal," said Coleman.
"I'd like to think it'd be done by January so once the transfer window opens we'll be in the mix with everybody else."
Meanwhile, defender Chris King has left the club after his contract was cancelled by mutual consent.