Go to this page: viewtopic.php?f=3&t=6286
There is a form that we use to record the details. I am sure it would be acceptable to any FBO for fuel discount.
I have also attached the form to this message.
I have never been asked for documentation on an animal rescue flight. I did have a large FBO at a large airport ask for documentation on an Angel Flight I flew so as to avoid a landing fee.