Police said they received a tip on a social media site that led them to the videos, which they said showed the suspect reaching speeds upwards of 115 mph.
The videos were posted by the user RiderLifeStyle, according to police. One of the videos on the user's page is titled "Yamaha R6 Runs From Cops- Full High Speed Chase!!"
They said they were able to track him down pretty quickly after they saw the videos.
"My first reaction was 'wow,' how did this person not wreck?" said Sgt. Ben Ford with the Mauldin Police Department. "The speed at which he was going, in and out of traffic, just very bold driving and dangerous driving."
Police seized a computer, files and a GoPro camera that was reportedly used to film the incidents, officers said.
"We really take serious the driving he was doing and we don't want others to congratulate him because people could die from that behavior," said Ford.
At a bond hearing on Thursday, a judge gave Kellett $445 cash bond on each charge.