According to TDB, the UAW hasn't had any representation on a board since Owen Bieber (no relation to Justin) served on the board of Chrysler in the 1980s. Bieber was allegedly voted off the board for voting against executive pay raises. The union has also has some indirect representation thanks to the Voluntary Employees' Beneficiary Association. General Motors and Chrysler each have a VEBA representative, though the board spots aren't affiliated with the UAW.
King hasn't given many specifics about any plan to add union representation on company boards and he hasn't outright called for The Detroit Three to agree to such an arrangement, but it looks like it may come sooner or later. The UAW contracts are up as of September, and there has been talk that King may want to negotiate with all three automakers at the same time instead of picking one target for pattern bargaining.