Graham Onions then removed Simon Katich and Graeme Swann bowled Ricky Ponting to leave Australia 25 runs behind at the close of play with eight second-innings wickets in hand.
"This is one of the few grounds I get runs at," added Flintoff. "I've done well in the past here and feel comfortable and it was nice to have a partnership with Matt Prior.
"It was a strange way to get out, caught off my glove off Nathan Hauritz, and I would have liked some more runs, but Stuart Broad batted brilliantly and we got a decent lead.
"Onions and Swann bowled great spells too and we're in this game. We know Australia fight all the way down and they will be thinking if they can survive the first session, they'll be able to save the game.
"But if we start well in the morning and get some momentum we believe we can win the match."
Aussies playing for draw - Hilfenhaus
Australia fast bowler Ben Hilfenhaus, who took 4-109 in England's innings, has backed his team-mates to save the game on Monday.
"We'll look to bat for as long as we can, hopefully we won't get bowled out but if we do hopefully we'll have enough runs on the board to hold on," he told BBC 5 Live.
"Shane Watson is in fantastic form with the bat at the moment, he's playing really well so hopefully I won't have to bat at all.
"I enjoyed having a bowl out there - when it swings around a bit I think the conditions are a bit better for me and the wickets are slower so you need to bowl a bit fuller.
"You've always got to learn, that's the nature of the game. They played some shots this afternoon and got away with it for a while, but we didn't execute our plans too well either."
Monday's weather forecast for Edgbaston is for sunny intervals during the late morning period followed by cloudier conditions, but remaining dry.
England lead the series 1-0 and there are two Test matches remaining after Edgbaston - at Headingley and The Oval.
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