I followed April L. Hamilton's free Indie Author Guide to create a linked table of contents for a Kindle DTP upload. It's a little outdated for my version of Word but easy to follow nonetheless. The guide goes through the whole process so is well worth a read especially if you're planning on uploading a book to Kindle for the first time. Tips include making sure each chapter or story begin after a page break and to remove all tab spaces. You can do this pretty easily by clicking CTRL + F, typing ^t into the find section and replacing all with nothing. So assuming your manuscript is otherwise perfect, this is how I (hopefully successfully) inserted a hyperlinked table of contents into my Kindle editions.
First of all, I selected each of my story titles (or chapter headings in the case of a novel) and changed the style to Heading 1. In my Word program, it's right there on the home tab, no searching but April's guide tells you exactly where to find it in older versions. You can modify Heading 1 to your taste.
I went to a blank page near the beginning of my book where I wanted to place the table of contents. In my case it was the page before the first story (chapter one). I clicked the Reference tab, then the drop down arrow of Table of Contents on the left and finally clicked Insert Table of Contents. A dialogue box popped up with some choices. I ticked the box marked Use Hyperlinks Instead of Page Numbers. I set "Show Levels" as 1 because I only used one sort of heading style. Deselect any page number options because they won't show up properly. I clicked okay and a Table of Contents was inserted. It linked to all of the story titles (chapter headings) I changed to style Heading 1. I checked all of the links by holding down CTRL while I clicked on each story title (chapter heading) in the new Table of Contents.
Edited to add: I obviously didn't opt out of page numbers on one of my books because once it became live on kindle, I downloaded the sample and saw the story titles all contained a number. This didn't show up in the html preview or in the Kindle preview so watch out for that.
I saved my document. Then I saved as a web page creating a new file. I was then able to view the document as a web page. Viewing two pages at a time really showed off the nice formatting due to the page breaks being picked up. I uploaded this html document to Kindle and republished. The preview looked fine. This new version should be available on Kindle soon. I hope the TOC works when it is live!
There you have it. Adding a hyperlinked Table of Contents to a Kindle ebook was super easy once I sat down and tried it. There are other ways, they might work better so have a look around at what other people do. Again, I have to note that this method does not work on Smashwords. I don't know why. I tried uploading the same file and it said the table of contents had an error. I read the newly updated Smashwords Style Guide and saw they state clearly that this method doesn't get picked up by them. So I followed their version which is slightly longer and will post that one next time.