Five-try Leicester kept themselves firmly in the Aviva Premiership title play-off zone after reeling off a 10th successive victory in all competitions on home soil.
Scrum-half Youngs, prop Logovi'i Mulipola and flanker Steve Mafi scored first-half tries to underpin Leicester's dominance of a game they controlled in terms of territory and possession, before centre Matt Smith's 58th-minute score sealed a bonus point and an Alesana Tuilagi breakaway effort confirmed the rout.
Gloucester delivered little more than a prolonged damage-limitation exercise, not only being suffocated by relentless Leicester pressure but also seeing Flood stage a masterclass of tactical kicking.
England's current back-up number 10 added four conversions and a penalty, and with Youngs controlling affairs at the heels of his dominant forwards in miserable conditions, Gloucester surrendered.
Leicester toyed with their opponents on the back of a rampaging display by number eight Thomas Waldrom, and rarely in the Premiership this season can one side have enjoyed such supremacy.
Gloucester were left to reflect on their heaviest Premiership loss since Quins thumped them 42-6 almost six months ago, but Leicester continue making a traditional full-scale tilt on more Premiership silverware.
Leicester, whose post-World Cup form had seen them lose just one Premiership game, welcomed back prolific try-scoring wing Tuilagi in addition to Flood and Youngs.
Injuries sidelined Gloucester centres Eliota Fuimaono-Sapolu and Henry Trinder, so Tim Molenaar partnered captain Mike Tindall in midfield, while wing Ollie Phillips answered a late call when England squad Charlie Sharples failed a fitness test.
Last season's Welford Road fixture between the clubs finished 41-41 - the highest-scoring draw in Premiership history - but driving rain and a heavy pitch made any repeat unlikely.
Burns struck an opening blow for Gloucester with a long-range penalty, although he missed from far shorter distance shortly afterwards as a gusting wind added to the goalkicker's degree of difficulty.
Flood almost helped Leicester wipe out their early deficit when his steepling free-kick caused chaos in Gloucester's defence and only a desperate last-ditch tackle kept Waldrom out.
But the number eight made his presence felt from closer range just three minutes later, taking a quick penalty that resulted in Mulipola grounding the ball underneath a pile of bodies.
Flood slotted the conversion for a 7-3 lead, and then his astute tactical kicking afforded Tigers an attacking lineout from which they prospered in the 23rd minute.
Mafi won the lineout, then surged 15 metres to cross Gloucester's line for a try that underlined Leicester's forward dominance against opponents battling to hang on.
It was superlative wet-weather rugby by the Tigers, and they went within inches of adding a third try after lock George Skivington and Waldrom broke clear, but Flood agonisingly failed to get the ball down.
He kicked a penalty, though, 11 minutes before the break, and Gloucester had it all to do, trailing 15-3 and offering next to nothing as an attacking force.
But there was worse to come, and Gloucester's first-half misery was completed when Youngs scampered 20 metres to score, courtesy of a sniping break that once again raised questions about Gloucester's defence.
Flood again added the extras, and a 22-3 interval advantage was way too much for Gloucester to fight back from.
And the game was finally put beyond their reach just before the hour-mark after centre Billy Twelvetrees' expertly-placed kick created room for his midfield partner Smith to finish off.
Tuilagi then struck when Gloucester full-back Jonny May's kick just 20 metres from the Tigers line went straight to the giant Samoan, and he galloped away without an opposing player touching him.
Flood again converted, and with the bonus point easily secured, Tigers boss Richard Cockerill could make a raft of substitutions knowing the job had been done in emphatic fashion.
Gloucester scrambled for a consolation try as the clock ticked down, but Leicester easily coped with anything they could offer as they concluded a thoroughly convincing afternoon's work.
In the day's other match Charlie Hodgson's six penalties saw Saracens grind out an 18-12 win over Northampton in tough conditions at Vicarage Road.
Stephen Myler kicked three penalties for the Saints and sub Ryan Lamb a fourth, but Saracens stayed on top to earn a win which puts them second in the table.