Flintoff, 29, stepped up his return from ankle surgery by playing in Lancashire's County Championship clash against Sussex this week and Graveney expects to see him in action against the Indians.
The all-rounder missed the entire Test and one-day series against the West Indies after his third operation to clear up the recurring ankle problem, but is on course to play in the first match against India on August 21 at the Rose Bowl.
"It's great that he's back playing," Graveney told BBC Radio Four on Wednesday.
"He's started to bowl in nets and there's nothing that I've heard to the contrary that would prevent him from playing in the one-dayers towards the back end of the month.
"Hopefully he will available for that, and he has certainly indicated that will be the case."
England's players were criticised for their conduct during the Second Test defeat against India at Trent Bridge, but Graveney insisted both sides must share the blame.
Zaheer Khan reacted angrily after jellybean sweets were left on the wicket by an England player as a prank while he was batting, while Shantha Sreesanth was fined half his match fee for barging into Michael Vaughan and also bowled a beamer at Paul Collingwood.
"There were issues on both sides, there were people bowling beamers and people bowling through the crease," Graveney added.
"There were some incidents I'm sure the match referee will have noted and spoken to both parties.
"India deserved to win the Test match and hopefully we move on to a really exciting contest at The Oval."