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."

A bottle of Deanston 12-year-old malt was broken over the bow of the 90-metre Offshore Patrol Vessel in a ceremony at BAE Systems' Scotstoun yard.
The ship is expected to go into service next year and will be used for counter-terrorism, anti-smuggling and defence.
The MoD said work on HMS Forth and her sister ships was sustaining 800 Scottish jobs.
The vessels will be equipped with a 30mm cannon, a flight deck capable of accommodating a Merlin helicopter, and will be manned by a crew of 58 sailors.
It is the first of a fleet of new Batch 2 River-class OPVs being built on the Clyde, which are all expected to be in service by 2021.
Their construction has filled a gap in the order books of the Govan yard, where work is due to begin on eight Type 26 frigates this summer.
The Type 26 frigate, which is principally designed for anti-submarine warfare, will partially replace the current Type 23 frigate.
Each ship will carry a crew of 118, have a top speed of more than 26 knots and a range of 7,000 nautical miles. The first vessel is due to enter service in the early 2020s.
Defence Secretary Michael Fallon said that the work would safeguard hundreds of skilled jobs until 2035.
HMS Forth, the fifth Royal Navy vessel to bear the name over the past two centuries, is affiliated with the city of Stirling.
The MoD said the name maintained a connection that began when the people of the city adopted a previous ship with the name Forth during World War Two.
Minister for Defence Procurement, Harriett Baldwin, said the programme to build the ship was a vitally important part of the government's 10-year, Â£178bn plan to supply the Armed Forces.
She added: "From counter-narcotics operations in the Caribbean, to securing the UK's borders on patrols closer to home, the Royal Navy's new Offshore Patrol Vessels will help protect our interests around the world."

Swiss-born Mira Andres, of Aberystwyth, will get Â£1,000 and exhibit at Swansea's Elysium Gallery after winning the ESPY International Award 2015.
The University of South Wales graduate was recognised for her composition, The Black Crows of Borth.
It was inspired by the women who once walked the coastal path to Aberystwyth to sell herring and cockles.
Ms Andres, 28, who works as a freelance photographer and designer, said: "I'm very honoured and pleased to have won and I'm looking forward to exhibiting more of this work."
She was chosen as winner by judges Helen Sear and Peter Finnemore, two leading Welsh artists who have represented Wales at the Venice Biennale exhibition.
Kent were denied their second win of the season as Gloucestershire held on for a nervy draw at Canterbury.
[NEXT_CONCEPT]
The first of a fleet of five warships being built on the Clyde has been formally named HMS Forth.
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A Ceredigion photographer has won an international competition with a series of pictures taken in Borth.