KKR, a New York-based private equity firm, has prevailed over other buyout firms in the auction for Air Medical and is now in the final stages of negotiating a deal with the company’s owner, Bain Capital LLC, the people said on Tuesday. KKR and Bain declined to comment, while an Air Medical representative did not immediately respond to a request for comment. Based in Lewisville, Texas, Air Medical operates a fleet of 222 helicopters and 25 airplanes from locations in 27 states.