If you have a blood transfusion and then have a DNA test will it affect the outcome?

It depends, yes in theory there will be foreign DNA in your blood stream (only due to white cells mixed in the red blood cell from the new blood) but that will have no permanent effect and since white cell count is so low the effect would be minimal for the test. Most likely the test will show not foreign DNA but in theory it can affect the result (but again this is very unlikely due to the very short time; and most likely second tests would be ordered if there are any problem).

But if the DNA sample is taken from other fluids like saliva or from skin samples, then the blood transfusion will not affect the normal DNA test.

Besides DNA technicians will be told if the person was in a serious accident or surgery.

By the way, this could be a good idea a for a CSI or Law & Order episode.

mature red blood cells don't have a nucleus, there is no chance for RBC to affect DNA testing as DNA's found inside the nucleus. (in line with this, there was a debate at some point regarding protein production in RBC)

If they swab the inside of your mouth as is often done here, blood transfusion is not going to interfere with the outcome.

if they draw blood right after the transfusion and your leukocyte count is not zero then you may appear as a chimeric individual but it's easy to discern

Well you will have the RBCs of another person as well as yours. So, yes but they should see that. When those donated cells die (within 120 days, then everything will be yours). For best results in that case, then get a cheek swab.

There's no DNA in RBCs and there's not enough detectable DNA in whole blood.