Kimbrel will want too much money. (1) Get the draft pick and spend the first 2-3 draft selections on position players. The Red Sox have some excellent pitching prospects, including Houck, Groome, Mata, and Shawaryn, but they need to strengthen their position prospects. They started doing this in June by taking Casas and Decker but they have more work to do. (2) There will be other options, cheaper options, on the free agent market that won't involve draft compensation, including D.Robertson and Z.Britton. (3) The Red Sox need to resign Eovaldi, a higher priority than Kimbrel IMO, and Eovaldi's price keeps going up and up. The Yankees, who are desperate for starting pitching, will probably chase him too.
Relief pitchers are too volatile from year to year and Kimbrel is getting older. The Red Sox have their future closer in Durbin Feltman, what a great pick by Dombrowski, but they need a bridge closer, a guy who can handle the job for one or two seasons.
Britton is a guy you might be able to get on a shorter deal, a one or two year deal. With his recent injuries, I don't know if he has a long term, lucrative contract waiting for him. The Yankees will have a hard time resigning Britton--they can't offer him the closer role while the Red Sox can!