Kilts in American Revolution

[Canadian Vet]

I was rather surprised to see Jamie Frasier wearing a kilt in the Battle of King's mountain in the TV series, Outlander. I would have thought kilts would have disappeared by that time in the colonies. This is partly of interest to me because I am interested in being a member of the Color Guard for the Sons of the American Revolution charter in Philadelphia. I went to the trouble of having one of my ancestors acknowledged by the group. Many members wear the uniform of Washington's Lifeguards or some variation of a militia uniform, however, my antecedents were from the Carolina militias that responded to the threat of Tarleton's threat to the peace of the back country so makes sense to me to wear something that reflects that tradition. I claim kinship to the Murray's whose tartan was defined by Lord George Murray prior to the American Revolution rather than being an invention of the Victorians.
I was wondering if wearing a Murray of Atholl kilt as a reenactor of a Revolutionary War militia member makes sense.

I wear Murray of Atholl and I am the son of Loyalists.