A transport vehicle which is chosen as part of a squad (a Space Marine Rhino or Imperial Guard Chimera, for example) cannot gain Battle Honours of its own (who ever heard of an Elite Chimera?). Transport vehicles which are chosen as a self-contained unit (like Eldar Falcons and Space Marine Land Raiders) earn experience just like any other vehicle, and roll on the Vehicles table for any Battle Honours they gain.
Transport Vehicles
Source: Core Rulebook 3E, p. 160