Since you are talking about DNA being on file (I think), here are some issues:
1) If your uncle has tested (or somebody has sponsored his testing), you would have to contact the current individuals who access the account, add your email to the account (added as another sponsor). Once your email is added, you would have known their FTDNA ID (not sure about other vendors). You could probably also place orders as well - but would have to change the payment options to your credit card or your paypal. You should still get an email for permission to test from the donor for each test that you order though.
2) If you want to make sure that you have the donor's DNA on file - before placing orders, you can order kits for collection and collect the samples up front - be sure that you get an email from the donor as well giving you permission to test his/her DNA. I think FTDNA will also store DNA as well. They do charge a minimal fee for the extra collection kits.
3) If you think that they have already tested and want to determine the kit number, you would have just send them an email directly or call them to get their ID. This would allow you to know their ID in case they match other relatives or yourself.