No, I know of no way to make a Kindle select the special cover document. I should clarify that you very well can change where a new book should first open. I meant that there is no control for that in Scrivener. It is recommended that a book start on the first page of the main matter so that a reader can get straight to it, but if for some reason you need to do otherwise you can set the start position to any section in the e-book. You’d have to get your hands dirty messing with the guts of the thing though. Easiest way to do that is to turn on the source file export option in the KindleGen compile pane. This will output a folder beside your .mobi. Go ahead and delete the .mobi as you’ll be making a revised one. Go into that folder and edit the ‘my_book_name.opf’ file. This XML document describes the “spine” of the book, it’s how Kindle generates a nice navigational system for it. At the bottom of the OPF, change the reference element within the guide element that has an attribute value of ‘title=“Start Here”’. The href attribute is what document the Kindle will use to open the book when it is first viewed. It’ll probably be something like ‘body4.xhtml’. The stuff before it are potentially your dedication section, preface, table of contents, and title page—front matter basically. If you changed it to ‘contents.html’ then you’d have the reader load up the book at the ToC. Changing it to ‘body.xhtml’ would likely change the default to the title page, or maybe the copyright page, whatever is absolutely first.
Like I say though, the cover is not an actual web page that you can specify here. It’s a special value more like meta-data is. It can’t be “linked” to. So what I have seen some publishers do is create a second cover page and link to that. It’s kind of messy, because if the reader goes back a page they’ll see another cover image, and it’s two big graphic files where one should ordinarily do, but that’s how it can be manually done. You can’t do anything with Scrivener though (other than making the dummy cover document, of course).
Once you’ve modified the OPF code, save and close the file, you’ll have to use the command line to execute the kindlegen UNIX program, specifying this .opf file. That will spit out a .mobi file if all goes well. Give it a try in Kindle Previewer and it should open wherever you want. You can set it to open in chapter 8 if you want. 