Zimbabwean Flower stepped down after the 5-0 Ashes drubbing around the New Year and used his first major interview since leaving the job to back Cook, whose captaincy in last month's test series defeat to Sri Lanka was widely derided.
"He is an outstanding cricketer and we, the English public, should be proud of having Alastair Cook as one of our own, leading the test side," he told Britain's Sunday Telegraph.
"It seems to be forgotten, and people should not forget, that this is a young man, a 29-year-old man, who has done some extraordinary things for his country," he added.
"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."
Flower said it was important not to forget that England had experienced great successes under Cook's captaincy as well as the recent failures.
"He's led the one-day side for a while now and has got the most one-day wins of any England captain," he told the paper.
"He's led the side to an astounding test victory in India, against the odds, and in the main on pitches which England have traditionally struggled on, and tactically he was excellent in India. If he hadn't been, we would not have won.
"He has led the England side to a 3-0 test victory against Australia.
"I know a lot of people have dumbed down that test victory but what would we not give for a 3-0 victory against Australia now? And this guy is only just embarking on his leadership career."
Although not alone, Cook's most vocal critic over the last 12 months has been Australia spin-bowling great Shane Warne, who described his captaincy in the second test against Sri Lanka at Headingley as the worst he had seen in 25 years in the game.
Warne, who made his attack in a column in the Sunday Telegraph's daily stablemate, suggested Cook step away from the captaincy, or even from cricket altogether, and concentrate on recovering his batting form.
Flower, though, said England fans should make up their own minds about Cook's captaincy and allow him the space to learn from his mistakes.
"They should not be duped into thinking otherwise by those that have the platform to shout loudest," Flower said.
"They should make their own judgment about a fine, proud Englishman leading the England cricket team.
"He would still acknowledge he is learning all the time. But who of us isn't learning? I know I've learnt a hell of a lot in the last couple of years and I'm 46.
"Who are the ignorant ones? Is it a guy like Alastair or is it the people who keep making the same mistakes over and over again in their lives?"
- Sports & Recreation
- Alastair Cook