Since Nigel Clough took over in October 2013 the Blades have won 13 of 16 cup ties, with their only loss coming in The FA Cup Semi-Final against Hull City.
Of those 13 victories, five have come against Premier League opposition, and Flynn says their continued success shows the quality they have among their ranks.
Preston North End v Sheffield United
FA Cup Fourth Round
3pm, Saturday 24 January
Winners receive £90,000
“It’s an astonishing record,” he said.
“Obviously last season was pretty unbelievable, the run we went on and the teams we beat. This season has been pretty much the same, with the League Cup as well, and it shows it wasn’t a fluke.”
Sheffield United’s FA Cup Fourth Round tie against Preston North End is sandwiched between two League Cup Semi-Final ties against Tottenham Hotspur.
They are also battling for promotion from League One, and sit seventh but with games in hand over many of the sides above.
And while Flynn says promotion will always remain their focus, he adds that the additional success in the cups can only boost their chances.
“Obviously the priority for us is the league and we want to take that form into the league,” he added.
“People think that cup football can be a distraction, but from my experience I’ve always found that the better we’ve done in the cups then it’s improved us in the league.”
As they prepare to travel to fellow League One outfit Preston, the former Liverpool trainee said that although another Premier League tie would have been preferable, they take on Preston with full focus.
“You can look at it both ways,” he added.
“In The FA Cup you obviously want to pit your wits against other teams in different leagues.
“But it’s going to be a difficult game. Some people might look at it as more winnable, but they’re flying high in League One so it won’t be easy.
“We always believe we can go out and get a result, against whoever we’re playing”
Ryan Flynn Sheffield United
“We played them recently in the league and we managed to get a victory over them then, but it was a hard-fought game – and we’re expecting the same again.”
And whether their incredible cup records has them going into every game as favourites now, Flynn was diplomatic in his response.
“I don’t think so," he replied. "But we do always go into them with confidence because of the recent results we’ve had.
“We always believe we can go out and get a result, against whoever we’re playing, and when you have that belief then you know anything can happen.”