During the Kingdom Kill Event, the Homeland Fortresses (those behind Faction Border) and the Citadels are closed to the Rival Kingdom. 

Moreover, you can only teleport your city to the Warzone of the Rival Kingdom. You can not teleport into the four Homeland areas protected by Faction Border. However, your army can march across the Faction Border into the Homeland area. 

Basically, the rule is the same as what it was before Faction War in a Kingdom.