It was a disastrous end to a great day at the Santos Tour Down Under for the 22-year-old, who is in his first year with BMC.
Flakemore joined compatriot Cameron Meyer (Orica-GreenEDGE) and Belgian Thomas De Gendt (Lotto-Soudal) in a break that formed 16km into the 150.5km stage.
They kept the peloton at bay until caught at the 24.5km mark.
Juan Jose Lobato (Movistar) won the bunch sprint to take out the stage and Australian Jack Bobridge (UniSA) finished 20th to retain the overall lead.
Flakemore, who finished 113th on Wednesday, was proving to be team mate Cadel Evans's most in-form teammate at the Tour.
This is Evans's last WorldTour race before he retires from professional cycling on 1 February.
Flakemore impressed the 2011 Tour de France champion with his strong ride to finish fourth earlier this month at the Australian road championships.
"As Campbell showed in the national championships and as he showed today, he is a fantastic guy for the race," Evans said.
"Just to get in that (breakaway) move was really clever and observant. He was really showing his maturity and looks like a rider to me who has the capabilities to utilize his physical potential, which is a pretty rare combination.
It is really unlucky for him after what he did today and in the national championships. I was just thinking after the race what a good job he is doing."
He joined BMC after winning last year's under 23 world time trial championship.
Evans rates Flakemore and new Orica-GreenEDGE signing Robert Power as having great potential to eventually become contenders in Grand Tours such as the Tour de France.