Opener Cook is facing increasing pressure ahead of the five-Test home series with India that starts next week.
The 29-year-old has struggled to contribute regular runs at the top of the order for some time, while his captaincy has been heavily criticised in certain quarters, particularly after England followed a 5-0 Ashes humbling at the hands of Australia with series defeats to Sri Lanka in all three formats of the game.
Seemingly infuriated by the level of condemnation coming Cook's way, Flower has launched an impassioned defence of England's captain.
"It seems to be forgotten that this is a young man who has done some extraordinary things for his country - for himself and for his country," Flower told the Sunday Telegraph.
"He has scored the most Test centuries for his country - that in itself is an amazing achievement, and he's got so much more left to give.
"He's got the most one-day wins of any England captain. He's led the side to an astounding Test victory in India [in 2012]. He has led the England side to a 3-0 Test victory against Australia [on home soil last year].
"He is an outstanding cricketer and we, the English public, should be proud of having Alastair Cook as one of our own. They should not be duped into thinking otherwise by those that have the platform to shout loudest."
Flower also revealed that the dual-coaching structure previously employed by England had been a major factor in his decision to step down after the 2013-14 Ashes.
Peter Moores now coaches England in all formats, but Flower had split his role with Ashley Giles, with the latter taking over the day-to-day running of the limited-overs teams.
"It was a huge sense of loss," said Flower of his feelings on resigning.
"When you throw your heart and soul into something ... I knew I'd eventually have to step away or be moved on, but I guess it was the manner of the defeat [in Australia] that was hard to accept. But it did seem like a perfect storm out there.
"Perhaps it was the time for change, in the best interests of the side, and my tanks might have been running a little dry. Also I don't think the press would have accepted the manner of our defeat without seeing some blood spilt.
"But the job being split was a huge part. I didn't see a way forward as we were. After a year of trying to make the two-coaches model work, it was obvious that it wasn't going to."