The son of embattled former Chelsea Housing Authority executive director Michael McLaughlin was fired today from his $60,000-a-year job on the state Board of Appeals, according to sources with firsthand knowledge. Matthew McLaughlin, who was recommended for the position in 2008 by Lt. Governor Tim Murray, was found to have falsified at least one time sheet, claiming he was working when he was actually away, said a source briefed on Matthew’s firing. In addition, Matthew sometimes claimed he was out of the office on “flex-time,” but the agency does not allow employees to work flexible hours, the source said.