Leeds travel to south Wales on Sunday sixth in the Sky Bet Championship and 53 places higher than Newport in the pyramid.
But Flynn believes Leeds will not relish the third-round trip as County seek to reach the last 32 for the first time in nearly 40 years.
“They will be out of their comfort zone at Rodney Parade, make no bones about it,” Flynn said.
“It’s an earlier kick-off, they have had to stay overnight, and they are coming to a stadium which, let’s be honest, is not as good as they are used to.
“That’s not taking anything away from them because they are a professional outfit and they will come here with the right intentions.
“But it will be different for them. I’d be surprised if the wind wasn’t swirling, maybe a bit of rain and the conditions will be difficult.”
The two clubs met in the Carabao Cup at Elland Road earlier this season after Newport had been unable to stage the tie because of renovation work at Rodney Parade.
Leeds recovered from a 1-0 deficit to win 5-1 that night, but Flynn feels the scoreline flattered Thomas Christiansen’s side.
“For anybody who went up there and saw the game at Leeds, they will tell you that we created a lot of chances and should have scored more goals,” Flynn said.
“Maybe it’s a little bit of fate that we have drawn them at home in two separate cups and now we finally get to play them at Rodney Parade.”
This is only the second time in 32 years that County have reached this stage and they have not made the fourth round since the 1978-79 season.
“I’ve said it all along that I want to build a club here and not just a team, and it will go a big way to helping provide a training ground for the football club,” Flynn said.
“I think that’s what it’s about – leaving legacies and doing what you can off the field.”
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