The children were taken to a hospital but their condition was not known Saturday night.
Brandon Robinson said he and his wife took their children to the fair. His children were in line for a inflatable jump 'n slide when the wind suddenly picked up.
"As I turned to my left I saw the first (bounce house) pick up about 10, 15 feet into the air," he told CNN. "I didn't see any kids fall out, but it came slamming right back down to the ground.
"About 10 seconds after that one picked up, the one right next to it just slung about 25 to 30 feet up in the air, got caught by the power lines, and hung there about 10 or 15 seconds."
The lines snapped and the bounce house fell to the ground.
He said he saw children from the first bounce house laying on the ground.
"They looked really hurt," he said, adding that he didn't think there were any children that were in the inflatable that flew into the power lines.
Sgt. Jimmy Bolt with the Greenville County Sheriff's Office said the incident happened about 2 p.m. at Springwell Church in Taylors, in the northwest part of the state.
Elvis German said he was working nearby and his children saw the bounce house take flight. "My kids yelled at me and said 'Look, Daddy,' and I saw the bouncy house caught up in the power lines. It was like 20 feet up in the air."
He said he grabbed his phone and started shooting video and "it made a big noise and the power went out when it fell."
Power was knocked out briefly in the neighborhood, said Lee Freedman, of Duke Energy Corporation's media relations department.
David Pearson, operations pastor at the church, posted a statement on Facebook
"This afternoon, we held our annual Spring Carnival on our campus," he wrotre. "Shortly after 2 p.m., an unexpected wind gust, out of our control, lifted an inflatable amusement that was on our campus for the event. We are saddened for those who were injured during the unfortunate accident today."
Injuries and deaths have occurred in similar incidents.
In March 2016, a 7-year-old girl died when a bounce house was blown away in Essex, England.
In May 2015, three children were hurt when a waterspout came ashore
and lifted a bounce house in Fort Lauderdale, Florida.
In May 2014, two boys from upstate New York
were hurt after falling nearly two stories when a gust of wind swept up the inflatable bounce house they were playing in, police said.