I make games on iOS, Android and Amazon. Although it is already bad on iOS and Android, on Amazon the results are so bad that if they were worse it would be negative.
Although my company needs to learn how to do marketing across the three markets, how do I learn about marketing on Amazon? How do I figure out the most effective marketing avenues to use there?
Look around at your top potential competitors and look at what they're doing. Find where they are advertising, where they're getting reviews, and generally how they're operating.
Unfortunately, only seeing the actions and (some) results doesn't necessarily give you any insight into their strategy and how it is/isn't working. It's like finding where a boat is by its wake. You can tell where it's been, but not where it's going.
Anyway, it should be enough for you to get some ideas, start experimenting, and look at the results.
Just be careful where you spend your time and money until you actually have some results to analyze. I don't know how many times I've worked with groups that are totally convinced they should do X and invest in it completely.. only to figure out that Y is 100x more effective. But then their budget is gone. :(