Protocol for Submitting Fellowship Application where I need to see my advisor's Recommendation Letter I'm applying to a graduate fellowship program that has extremely strict rules about submission, and I must submit my application as one PDF, including my letter of recommendation from my advisor. He's written me several letters before that I haven't seen, but how am I supposed to ask for this letter?
Just ask.  Tell him the rules of the fellowship application (with a link so he can verify) and ask if he's comfortable writing a letter that you would be able to read.

If he's not (and this would be an entirely reasonable position), see if you can work out something else.  For instance, you might be able to send all your other materials to your advisor, or to some third party such as an administrative assistant, who would compile everything together with the letter and submit it on your behalf.  Or you (or better, the professor) could contact the fellowship funding organization and explain the situation, and ask if they can suggest any alternative methods of submission.

In the worst case, if there is no way to resolve the conflict, then you simply won't be able to apply for this fellowship.  Seek out others.