The Kit abilities that the popup text is referring are the Ground abilities that you can train BOFF in. The abilities are in the player Kit equipment that you equip onto your character. In essence your BOFFs "Kit" are the 4 ground abilities that they are trained on.
In some ways BOFFs are more flexible than player's Kits as you can put any skill you can fit into a skill slot. Whereas player are stuck with the predefined Kits are our Ground abiliies (outside of the Captain only abilities).