His naturally ruddy countenance is merely a symbol of his winning ebullience as a player. Many, if not most, professional sportsmen say they still enjoy playing; Fleming transmits both the pleasure and the relief that he is not doing something else much less alluring.
For 10 years he has performed with rubicund gusto as a county all-rounder and when he was summoned to play for England the day before his 33rd birthday, to his own and widespread surprise, he did precisely the same. Although he states in the latest edition of Cricketers' Who's Who that there are too many opinions on the game and not enough action, he has opinions in abundance and as chairman of the Professional Cricketers' Association is unafraid to express them.
Last week at Lord's he captained Kent for the first time. The Long Room could probably feel his exultation as he led his team through on Tuesday morning. "I had always wanted one day to be the captain since I joined the county as a player," he said. "I suppose I thought it had passed me by and if we had won three competitions two seasons ago instead of coming second in three I know I wouldn't be in the job now, that is for certain.
"But once you've had a leadership role it can be strange to be reduced to the ranks as it were. You want to lead. I'm not saying I'm any good at it, I'm aware I have shortcomings but it was an ambition to do it. My mother is a great believer in fate and always said you have to want things enough. Well, here we are."
The leadership role which Fleming used to fill was as a lieutenant in the Royal Green Jackets. His short-term commission took him on tours of duty to Northern Ireland and Hong Kong. "I would be lying if I said I made a lasting impression as a soldier," he said. "I had an understanding commanding officer who realised that the regiment improved in line with the number of times I was away."
Fleming resorts regularly to self-deprecation. Perhaps it is his way of recognising limitations but it should not conceal his ambition or resolve. He made himself into a county cricketer by a mixture of determination and exuberance after he had failed to impress in the Kent nets soon after leaving Eton (for whom he appeared twice in the match against Harrow at Lord's, in the second scoring 52 and taking 1 for 1 in eight overs).
During his army service he was allowed to play regularly and made frequent appearances in the county second team. He progressed enough to earn a full-time contract and has rarely been out of the side since, averaging 30 with the bat, a little more with the ball, fielding hungrily. He remains one of those players whose superior talents are not blindingly obvious - as he would self-deprecatingly admit - but for the way he has played he can be forgiven much.
His first two scoring shots in first-class cricket each went for six and he has continued to go for the big shot and to try to deliver the wicket- taking ball. Being captain might slightly arrest his gallop in this regard. It was noticeable when he batted against Middlesex on Thursday, for instance, that the free-range strokes had been reined in. He was the model of riskless propriety, a world away from his free-spirited nickname of Jazzer. If it is a seminal season for Fleming and Kent, that also applies to the game at large. The World Cup looms large, the domestic game is being revolutionised.
"We are in the entertainment business, of course we are, and players realise that," he said. "I don't think we will ever fill grounds again at county level but there are 20 million people in this country who are interested in cricket and 160,000 who are county members. That is a quite disgraceful disparity and there is obviously something wrong.
"County wages have gone up dramatically in the past five years and that's probably because of television. The players know that but most are still only employed six months a year. If we are to be effective the entertainment is extremely important, but winning is extremely important.
"The balance is a difficult one to achieve. If our primary role is to produce a strong England then entertainment is correspondingly less important and winning more important. In fact the role of county cricket is somewhere in the middle but nobody as yet seems quite certain what the role should be."
They had better discover pretty quickly, as Fleming conceded. He is not of the persuasion that time is running out for the old game but he knows that it needs its confidence replenishing (and whatever the gut feeling says about winning, it probably needs a bit more of the Jazzer approach). "The positive effects of the World Cup this summer cannot be overestimated," he said. "If England win it, and I think that they can, it could do more for cricket than anything since Ian Botham's England took the Ashes from Australia, and those sorts of things come along once every 25 years. [If he is right about the timespan we are unfortunately seven years short since Botham's Ashes were in 1981.]
"But there is more to be had from the upside. If England were to do badly it wouldn't be good for the game but I don't think it would be terminal. The danger is that the game would just fizzle. But I can't stress enough that the upside is greater than the downside.
"I'm not entirely in agreement with the team that the selectors have picked but that doesn't mean I don't want them to win or that I think they can't win. They can. And don't forget that everybody has opinions on this."
It might be Fleming's own assessment that he ought to be in the 15 himself. When he was called up for the Sharjah tournament in December 1997 he had assumed, like the Kent captaincy, that England had passed him by. But his ebullience was immediately noticeable. He loved being there and it was possible to love him. But his international career appears to have ended at Headingley last year.
"I played 11 times and of those only two could really be described as bad games," he said. "I don't think I let them down when I played. I was disappointed not to be picked for the World Cup but there's nothing I can do about it. I haven't dwelled on it."
Now he is the captain of Kent, who have been without a trophy since 1978, he claims no great visionary plans. "We're not going to start running four laps backwards or anything like that. I've had great help from the senior players already. I don't think perfection exists. All we can do is strive for excellence."
Most of the PCA membership - though there is, he said, "a divergence of opinion" - are in favour of two divisions. Fleming knows that his elevation to the captaincy will probably stand or fall by whether they make the top half and therefore the first division.
"We have the players but I can only do what managers in any organisation do. Get them to realise the importance of taking individual responsibility for the team and realise their own strengths. We have tended to concentrate more on the end result than the process of achieving it in the past and we'll be paying more attention to the process this summer."
Kent drew their first match under their new captain on Friday evening. It did not quite live up to Jazzer's expectations, but it will not have removed the colour from his cheeks.