With no play until 13:45 BST, the hosts declared on 478-8, a lead of 141, with 63 overs of play available.
Calum Haggett's destructive spell of 3-13 from nine overs reduced the visitors to 132-6 with 21 overs left in the day.
Jack Taylor (46 not out) and David Payne's (20 not out) unbeaten 53-run ninth-wicket stand saw Gloucestershire hold on as they finished on 211-8.
Kent captain Sam Northeast told BBC Radio Kent:
"The emotion from the team is of disappointment, but they shouldn't be really because we've played all the cricket.
"I'm very pleased today with the effort from the bowlers on a pretty flat pitch. They bent their backs and nearly got the result.
"We came so close and if it wasn't for the rain we probably would've got it. We're near at the moment, we're playing good cricket, which is a positive sign."
Kent were denied their second win of the season as Gloucestershire held on for a nervy draw at Canterbury.