I called Flagship Resort and they said No, they do not take them back(NO surprise there)but they will send me the names of some companies that will help me sell it.
If National Cancellation and Transfer was one of the companies recommended by your timeshare company, then they're probably OK. It would be important to read all the fine print before you sign anything, of course.
Now, if I list it and it sells, then what? If I were to list in on TUG or Ebay and someone wanted it then what should I do next?
What I did was as follows. Before I even listed the timeshare on TUG, I researched the timeshare's process for transferring ownership to make sure I understood it. They had a fairly convenient online process, so that was good. But, as is typical, they did charge a transfer fee ($400 in this case) and they did reserve the right to disapprove the buyer. If that happened they would not refund the transfer fee, so there was some risk there.
Then I browsed other people's TUG ads for similar shares in the same timeshare so I could write an ad that would be competitive. I also read TUG's articles about how to sell a timeshare, which were very helpful even though the news they shared was generally not pleasant. To have any chance at making a sale, most sellers had to (1) make sure it was bought and paid for - no loans outstanding, (2) be up-to-date on the dues and maintenance fees, (3) set a sale price of essentially zero, and (4) agree to pay all the transaction costs. I don't know how it is now, and of course I have no idea how much in demand your timeshare is - that's why it makes sense to browse the other ads before you write yours.
When my buyers (a couple) told me they were ready to buy, I asked them to sign a purchase-and-sale agreement that I'd written up and to send me a copy of one of their driver's licenses. That wouldn't have protected me from losing the $400 fee if the timeshare had decided to reject them (or they had changed their minds), but at least it let me communicate clearly all the details of our deal and gave me some reassurance that they weren't complete flakes. It turned out that they were already owners in that timeshare and were just wanting to add points, so I think that significantly reduced the risk that the timeshare company would reject them.