Tigers director of rugby Cockerill was angry that Lancaster commented publicly on Flood's ankle injury, which has left him in doubt for Leicester's Aviva Premiership final against Harlequins a week on Saturday.
As a direct result, England's most senior physio, Phil Pask, was barred from examining Flood at the Tigers' training ground on Wednesday.
Lancaster had described Flood's situation as "uncertain" ahead of England's three-Test tour of South Africa, although he had expected Pask to provide an update.
Lancaster also indicated that Flood would need to be fit for the first Test on June 9 if he was going to be considered for the tour.
Cockerill described Lancaster as "naive" and he will contact the new England coach to explain his frustration within the next 24 hours.
"It's very unhelpful really," said Cockerill, who remains optimistic Flood will be fit to face Harlequins at Twickenham in Leicester's eighth consecutive Premiership final.
"He is on club duty, it's our business and it's not helpful that there is speculation surrounding his fitness.
"It's inappropriate talking about it as I wouldn't talk about one of our players while they were on Test duty. It's not my business to do that.
"He could have said 'He is being treated by his club and we hope he will be fit for the final'.
"You don't need to start talking about time frames and when he might be fit.
"That is privileged information which should be kept between me and the medical staff. That is not to be discussed openly 10 days before a huge game."
Cockerill was frustrated that Lancaster commented on Flood but made no mention of Danny Care or Ugo Monye, two Harlequins players who missed the semi-final through injury.
Lancaster was not asked about Care or Monye at the Tuesday press conference in question.
Cockerill said: "There is lots of speculation but none about Ugo Monye or Danny Care who could miss the semi-finals. It's a bit odd but I will speak to Stuart about that and get it resolved.
"I haven't had an injury update on Care or Monye. Have you?
"So why is he talking about Flood in that manner and not the rest of the squad? It doesn't seem right to me and it is not his business at this point."
The Rugby Football Union are privately disappointed by Cockerill's actions given Lancaster has worked hard to forge close working relationships with the 12 Aviva Premiership clubs since he took charge.
It is not the first time this season that Leicester have clashed with England. The Tigers were critical of England's handling of Flood and Ben Youngs during the RBS 6 Nations.
Leicester also claimed England, then under Martin Johnson, had rushed Youngs back too quickly from a knee injury so he could play in last year's World Cup.
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