The accompanying caption on the clip said: "I said no [heart emoji] #patriarchytingz."
Responses were mixed, with some viewers furious at the airline's demand while others doubted whether the passenger was being truthful.
"That's ridiculous @alaskaair, do better," one person wrote.
"#cancelalaskaairlines," another said.
Others said they had experienced a similar response from flight attendants.
"Wait this happened to someone else I know too," another added.
Others were less swift to jump on the cancel bandwagon.
"You agreed to their rules when you purchased the ticket. Go read the fine print," one person wrote.
Others asked how she had been allowed to board the flight.
"The gate attendant told me to cover up, I said no," the woman commented back. "Her coworkers stepped in to help me and tell her it wasn't necessary."
Similar instances have been reported across the ditch. Recently, a former Love Island contestant claimed a male flight attendant said her outfit was too revealing and she needed to cover up.
Amelia Marni, who also works as a model and influencer in Sydney, posted a video of herself before boarding a flight. Soon after, she shared a second video, complaining that her khaki pants and a crop top had caused trouble amongst the airline crew.
"We love a s**t shame moment. A male flight attendant just told me to cover up and my clothing was too revealing. I can't wear this and it's inappropriate to wear on Jetstar. NEVER heard of this," she wrote.
A similar outfit to the one that got Marni told off by crew.
Later, Marni posted images of Jetstar's clothing requirements.
"Please refrain from wearing any clothing or carrying personal items that display words, images, symbols or slogans that may reasonably be deemed offensive," it said.
Unable to find any rules that meant her outfit was inappropriate, the 25-year-old joked, writing, "love a man abusing his authority".