If you're new to web design I think this is something that would take more time than it's worth in terms of how much money you get out of flipping a site. That said don't let me discourage you from trying it at first as a hobby. If you find it works for you, good on you, keep doing it.
Don't stick to just ebay and fleecebay. A simple search on google for "website's for sale" will bring up plenty more places to look.
I think you'd have to be really good and really clever to make this work.
Keep in mind you can find amazing website templates for under $100 + hours of personal time spent hunting for them. Or you can get a cheap designer to redo a site for you... probably $300-600. Or a really talented web designer would usually run $1000-3000 a site - for the most part the product these types create is worth the money. These people are generally artists in their own right. Or you can be a do it yourselfer
You don't just want to flip a website's look though. You want to improve it's content (content is everything). You want to increase it's search engine ranking... but the fact that the domain name is under new ownership is a minor penalty against your google page rank until you have owned that domain for a year. I "believe" (but don't quote me) if a domain changes hands more than once in a year the penalty is slightly worse, wondering why no one keeps this domain for long. Again, once the last person holds onto the domain for over a year the penalty should be lifted.
Here's a few major DO NOT's if you do this:
When you start working on a new site DO NOT immediately take down the old site and put up some under construction page. Do not delete a single page... do not empty out an old forum database. There may be links to those pages all over the place and in peoples personal bookmarks. If you delete any files you remove your links to a lot of your repeat traffic. If you do want to remove a page or replace it - use a 301 permanent redirect (see google for more info). Do not leave multiple copies of the same page up under different file names. Search engine's see this as duplicate content, and they don't like it. Do some research on google about other search engine optimization techniques. Beware though some techniques are myths and some are permanent rumors that no one but the search engines themselves will ever really know.
If you decide to try flipping some websites I wish you the best. You could learn a lot from doing this.