I'm think I understand your question - so let me take a stab at it.
First you have to identify correctly the donor and the recipient organ and how it interplays with immune system. We can receive different of organs (doesn't have it's own immune function), or on the other hand receive a bone marrow transplant (has it's own immune function)...
So the only time a donor transplant will attack a host is when you have bone marrow transplant, and now the WBCs from the donor confers immunity of the person it was donated from.... and the recipient in this case would be seen as foreign... and as you recall, the WBCs do this by looking at the HLA (human leukocyte antigen) on the cells its surveying to identify it as self or non-self. So if your receive blood cells that's not urs, then every organ will now be denoted as foreign and attacked....
Now to get back to your question.... since you are receiving a foreign organ... your immune system (WBCs) will see the kidney as foreign and then try to attack it (the degree of attack on that kidney would depend heavily on how much your HLA matches)... the closer the match, the less rejection your immune system would have for that received organ. All cells have antigens, and until the kidney cells die off completely and is removed from your body, you'll always reject it.