The long-serving winger crossed in both halves for Clive Griffiths’ side and also added nine points with the boot as Knights eventually proved too strong for part-time Richmond.
The visitors - without a league win since October - had impressed in the first period when they only trailed 5-0.
They had chances to score but failed to take them and clinical Doncaster - who kept their opponents scoreless until the 75th minute - made them pay after the break.
Knights almost scored immediately when Rory Pitman charged clear at the start of the second period but the big No8 was brought down just short.
Welshman Pitman, who signed a new deal earlier this week, made another break soon as Knights - clearly pepped up after an insipid first period - upped their game but again there was no finish.
They did, however, manage to add a penalty, Flockhart converting from in front in the 47th minute and soon after he added his second try with a fine effort.
His side ran back a poor kick and swift hands saw them create the space for Flockhart to race in from 25m out.
Doncaster began to exert pressure in the scrum and, with far better handling, started to create their opponents all manner of problems.
Centre Lloyd Hayes, back in the side after Will Owen suffered a broken hand, shrugged off a tackle on the hour mark to race in for their third try and scrum-half Tom James claimed the bonus point six minutes later.
It came from a well-worked set-move - one used on them to devastating effect by Yorkshire Carnegie last month - where Pitman ran infield from a line-out pretending to have the ball.
It fooled the Richmond line-out who all followed - leaving space galore for James to ease his way through.
Flockhart improved and did so again after claiming his treble in the 69th minute, collecting Elliott Creed’s clever crossfield chip to make it 34-0.
Doncaster’s hopes of a first clean sheet of the season were dashed when Callum Sirker ran in a 50m intercept which was the least the visitors deserved; they had largely dominated Doncaster in the first half.
Granted, Knights did take a sixt-minute lead, driving forward from a line-out and then full-back Stevie McColl’s lofted chip bouncing up perfectly for Flockhart.
But Griffiths’ side spent most of the rest of the half in their own half, battling to hold Richmond back.
Their line-out only worked sporadically, hooker Ben Hunter struggling at times with the wind, while twice they wasted good positions to attack with poor passing.
Tom James saw one go behind three of his own players and roll into touch while Hayes - who got through a ton of work defensively - threw another wayward effort that saw a retreating Ollie Stedman bundled into touch on his own 22.
They needed Josh Tyrell to be alert thereafter, the Knights lock stealing possession and running clear just when Richmond’s line-out seemed set to roll over.
The home side stole another soon after when penned in their own corner and Hunter had already produced a try-saving tackle on David Spelman when the Richmond tighthead ignored a glaring overlap.
The visitors self-imploded, too, with a couple of quick tap penalties that resulted in nothing, fly-half Rory Damant - who missed an early kick at goal - turning down an easy chance in front of the posts to instead throw an awful pass towards his winger that ended in touch.
Still, even when Doncaster had chance to go on the attack, they failed to take it, McColl missing touch with his kick as they headed for the corner just before the break.
However, it was a different story and a different Knights in the second period as they produced arguably their best half of rugby all season.
Doncaster Knights: McColl; Flockhart, Creed, Hayes, Lewis; Olver (Foley 74), James (Seniloli 67); Hislop (Williams 70), Hunter (Mayhew 52), Quigley (Sproston 63), Tyrell (Challinor 63), Civetta, Stedman, Calladine (Jones 71), Pitman.
Richmond: Dennett; Sirker, Ward (Kirby 63), Hudson, Rath; Damant, Jones L; Goodrick-Clarke, Freestone (Corradi 62), Spelman (Trenier 49), Warden, Lenygon (Crawford 56), Parker, Liston, Davies.
Referee: Andrew Jackson (RFU)