Burns' wife's role in the company was not immediately clear.
Chase Burns was released from the Caddo County jail on a $500,000 bond. He denied any wrongdoing.
"What we do is legal," he told The Oklahoman on Monday.
His father, Tony Burns, also serves as his attorney. Tony Burns told the newspaper that his son broke no laws.
"What Chase was doing was he was actually selling the Internet time," Tony Burns said. "That's was what his business was — providing the software. And there's nothing illegal about providing software to any business."
Tony Burns did not return a call seeking comment from The Associated Press.
A telephone number listed for Allied Veterans in St. Augustine has been disconnected. Multiple emails sent by AP to an address listed on the group's website weren't returned.
Former Florida state Rep. Scott Plakon, a Republican, said he filed bills to shut down internet gaming sites in 2011 and 2012. He said he first found out about the storefronts when one opened next door to where he got his hair cut.
"I found that this is gambling, happening right next door to our Publix (grocery store) and dry cleaner and it just didn't seem right," he said.
The former lieutenant governor — who is the mother of Miami Dolphins defensive back Nolan Carroll — has been named in previous scandals.
Last year, a former aide, Carletha Cole, claimed to have found Carroll in a compromising position with a travel aide inside's Carroll's office.
Cole is charged with violating state law for allegedly giving a recording of a conversation with Carroll's chief of staff to a newspaper reporter.
Cole said she was ordered by the travel aide to find adjoining hotel rooms for Carroll when they traveled. Carroll has said previously the allegations are an attempt by Cole and her attorney to get the criminal charges against Cole dropped.
Carroll, a married mother of three, became the brunt of late-night talk show hosts when she defended herself against the allegations, telling a Tampa Bay area TV station that black women who look like her "don't engage in relationships like that." She later apologized for the remarks, which implied that black lesbians are not attractive.
Associated Press writers Curt Anderson and Kelli Kennedy in Miami and Tamara Lush in St. Petersburg contributed to this story.