As an R4 or R5, when kicking members out of the alliance, is there a way to teleport their base so..

The only way to make it teleport is to attack it and zero it (reduce the durability to 0). This will make it randomly teleport to a new location. You could always message them and ask. Or let them know they need to move to avoid being attacked. If they are not active then attacking will do the trick.