You should send items to:
Office of Veterinary Admissions
School of Veterinary Medicine
Tuskegee University
Tuskegee Institute, AL 36088
This is the complete address. Anything that requires a signature is not a good idea, delivery confirmation should be fine. By the way in your post it said to send transcripts, just in case you were not aware the transcripts must be sent directly from the school they are coming from. You can't mail them your self. Also this information is on the online application, which you should be using. It was started last year and I know people applying later in the year were told they had to use the online system, even if they mailed a paper application. If you don't have enough space in the lines provided you need to write in the space to see additional pages, then mail that in. I did a paper application and the online application last year because I had far more information than could fit into the space provided on the online application. Also call and talk to the admissions person, Dr. Eljack, his phone number is on the website under the faculty and staff directory.
BTW the people who sent the online application had an easier time with checking status of the application and found out about acceptance sooner, because you can check all of this online after submitting the online application through-out the application cycle.