Hi Balderdash,
Check out the fellowship ads already posted on this forum- like the ones for Columbia, Hopkins, etc. They will give you an idea of what will be asked of you. In general, they will want a CV, personal statement, board scores (step 1 and 2), 3 letters of recommendation, dean's letter, and med school transcript. It will be much more efficient if you have everything scanned and ready to submit when the time comes. They really like it if you have done research before. Even a month of solid research will make you a good contender. Be able to tell them that you have written a proposal before and submitted to IRB before.
When you interview, ask them where former fellows have gone (and how long it took them to get there) and ask to speak with former fellows. They know you want to go to derm and you want to make sure that they will be able to be good mentors for you who will support your application later on. So far in all the the interviews that I have had, they discussed the strengths and weaknesses of my future derm application and told me that they would sit down with me later on to prepare me to answer some tough interview questions.
So to answer your question, they will ask for pretty much all the same stuff as the residency application because they intend for you to go to derm eventually...at least that was my impression so far. They want to pick good people who can do the work and who they can endorse later on. It reflects well on them when you get in and will make it easier for them to recruit good candidates later on when you leave...so they want to screen you to make sure you even have a chance of getting in to begin with.
Best of luck!