Fleck was stretchered off just after half-time and is now expected to be ruled out until March 2004.
After the game coach John Connolly said: "It is a serious injury, but not as bad as we first thought. He has a broken tibia and a dislocated ankle and was operated on last night. He should be out for around 16 weeks."
"Are thoughts are with Robbie at this moment, but he is determined to get back and we are all relieved that the injury is not as bad as initially feared" he added.
The game – played at Kingsholm – got off to a furious start, with 21 points being rustled up within the first 13 minutes.
Gloucester inside centre Henry Paul opened the scoring in the third minute through a well-struck penalty and he repeated the dose just five minutes later, adding another three points for a 6-0 lead after eight just minutes.
Olly Barkley finally put Bath on the board with a penalty of his own after 10 minutes, but that was soon cancelled out after Gloucester right-wing Marcel Garvey got over for a try.
Paul missed the extras, but it did not matter as Bath hit back straight away, Barkley running in a try, which he managed to convert – leaving the scoreline narrowly in the home side's favour at 11-10.
Paul stretched that lead to four points a few minutes later with another penalty goal, before Barkley's second penalty left the half-time score at 14-13 in the 'Cherry and Whites' favour.
The second half sprang into action pretty quickly when New Zealand-born centre Robbie Kydd, who came off the bench, dotted down after just six minutes.
Barkley added the extras again as Bath went into the lead for the first time in the match. Bath never relinquished the lead again, despite some powerful surges from Gloucester, who are under the leadership of South African-born flanker Jake Boer, with last season's skipper, prop Phil Vickery, on Rugby World Cup duty with England.
For Gloucester:Try: GarveyPens: Paul 3
For Bath:Tries: Barkley, KyddCons: Barkley 2Pens: Barkley 2