Any way to promote Kindle Select book to borrowers?

None that I am aware of.

There's an option to have the Select program promote your book for five out of the ninety days. I did it but it didn't result in the tsunami of sales I had hoped for.

From what I've heard, your best bet is to simply send copies of your book to reviewers. That's how some others got started.

I'm wondering the same thing. It seems so random the way some books skyrocket on Kindle while others don't generate much interest at all. I thought maybe there was some secret the successful authors knew to promote their books, but if there is they are keeping it to themselves.

I think the "secret" is to write a good book that has been edited, has a good cover, has a well-written and enticing description (blurb), and a reasonable price. Add to that some patience, persistence and a few reasonabe expectations and you may have some success. There is no guarantee. It is hard work. And, while you're doing all this, start writing your next book.

As far as promotion goes, you can jump down the sidewalk bouncing on your head and holding a balloon labeled "Look at me!" Perhaps you'll be noticed among the thousands of other authors who are jumping down the sidewalk bouncing on their heads and holding "Look at me!" balloons.