I'm not an expert, but just some thoughts here in case these are useful.
If you're releasing anything into KU (or indeed onto Amazon generally / other platforms) then it needs to be a complete work, in my opinion. Some writers have found success with serials, which are clearly and explicitly labelled as such, but these are planned and complete stories. It does depend on the genre, though. Writers with serials also seem to have a regular, rapid release schedule to maintain momentum.
What you're describing sounds more like teaser chapters or snippets? I know of successful authors who do snippets, teasers, deleted scenes, etc, to very good effect, but these are via their newsletter / blog / Facebook page and to an existing fan base or readership.
The normal advice on building a mailing list is to have something exclusive to give to people who sign up for your mailing list / newsletter. I haven't done this yet - I'm working on a short prequel for my next series - but others have used Bookfunnel as a delivery platform and Prolific Works to build up a mailing list by giving away free short works in return for a mailing list sign up.
If the story is already available in KU, then I would think KU subscribers would just download it there.
Building momentum in KU will also depend, I think, on your genre, normal length of works in your genre and what readers expect by way of a release schedule.
Hope some of this is useful.