I don't know of any military barracks in Covington, except those buildings that were put up at the sites of various battery positions, to house the permanent garrisons there (not any large barracks complex).

Perhaps the author meant the Newport Barracks, which was a long-standing establishment at the mouth of the Licking River. Some folks not from around there may have considered everything on the Kentucky side of the river to be "Covington" (I've seen this before in period writings).

Geoff Walden