“I want my rights and I want my career back,” Joslin wrote in the post.
The NPS confirmed that several employees were facing administrative action “for failing to follow National Park Service regulations”.
A spokesperson said there were “possible criminal charges against several park visitors who are alleged to have violated federal laws and regulations related to demonstrations”.
The Trump administration has introduced a host of policies attacking transgender rights since his second term began in January.
Joslin told The Associated Press they hung the flag “because there were a lot of policies coming from the current administration that target trans people”.