Former England spinner and Ashes-winner, Giles will begin his first assignment as specialist limited-overs coach when Cook's team return to India after Christmas. Team director Flower will remain in charge of the Test squad, as he is at present for the series against India which continues with the third match of four at Eden Gardens on Wednesday.
Cook believes the same strategy which split the workload and allowed three different England captains to concentrate on a format each, until Andrew Strauss' recent retirement, will prove a winner for the coaching staff too. Asked whether Giles' appointment could conceivably diminish Flower's authority, England's Test and one-day international captain said: "Not at all."
He added: "It is very clear that he is still the team director, and to me it is very similar to what happened with the three captains. That worked well, and there is no reason why this can't work well with the people involved. Having three captains gave new energy to each form of the game, and I can see that happening here."
Cook concedes the ground-breaking policy - England are the first national team to go down this route - will have to be tested.
"The coaches will have a little more time to prepare for each series," he said. "It is new, so it is virgin territory, but I can't see why it won't work really well.
"It's great that we've managed to keep hold of Andy - he's a great person to be involved with - and we're also adding more experience into the coaching team with Ashley coming on board. It is exciting times."
He is a great admirer of Giles, too.
"What he has got is a lot of success at Warwickshire - he's turned that club around," Cook said. "He is a really good character; he knows what it takes to succeed at international level.
"He did it the hard way as well. He would probably be the first to admit he wasn't the most naturally gifted of cricketers but, my God, he worked hard to get results. I assume he'll be carrying that into his coaching as well. I'm really looking forward to working with him."