The nephew of the reality TV star was arrested with two other boys for the blaze that tore through the Kruser-Finley House, near the corner of Richmond and Arthur Kill roads in Historic Richmond Town, on Aug. 28, the Daily News said.
The two other boys were aged 13 and 15. Their names were not released because they're minors.
The FDNY tracked down the three alleged arsonists after one of them bragged about starting the fire on Facebook, according to the Daily News.
The blaze destoryed the roof and damaged the second floor of the home, built in 1790.
Ed Wiseman, Historic Richmond Town's director, told DNAinfo New York in August that the home was unfenced and easy to get to, but the site had not been a target for vandals or arsonists before.
“This is the first time ever that we've had a fire in any of the buildings,” he said. “We are not a site that is normally targeted for criminal activity.”
The three face charges of arson, criminal mischief, burglary, reckless endangerment and criminal trespass, the Daily News said.