Many of the objects of this novel, like many of the minor characters, have their greatest function in moving the plot forward. This is, after all, an adventure story, and fast pacing is key. So we have Alan's French clothes, which identify him as a Jacobite to Hoseason and as Alan to the rest of the Highland world. And we have Alan's silver button, which says "Alan Breck Stewart" to all of his friends.
The Highland tartans are also symbolic forms of identification. These are the plaids that are used to mark the different Highland clans at a glance. In Kidnapped, what's weird about these plaids is that they are really visible in their absence. In the aftermath of rebellion, the English have legislated against them in an effort to break apart the clans. To get around this law, Davie observes Highlanders with imitation tartan patterns drawn on their pants, or with kilts that have been stitched together in the middle like some kind of undivided pair of plaid shorts.
This fact about the tartans goes from being an interesting cultural observation to an important plot point when we get to the murder of Colin Roy. Davie notes that Colin Roy's servant is wearing tartan, "which showed that his master was of a Highland family, and either an outlaw or else in singular good odor with the Government, since the wearing of tartan was against the [law]" (17.8). This tartan-wearing servant, proof that "his master [is] in singular good odor with the Government," is the first sign we have that the man passing in front of Davie is the King's Factor, his representative in the area.