Just got this in my email and figured I'd pass it along to anyone else who's never used the Amazon App before and hasn't looked in their Promotional Emails lately. Not sure the protocol on posting something like this, but wouldn't want anyone to miss out on it.
Seems pretty straightforward and is essentially a "deluxe" version of the old $10 for using the app for the first time promo. In addition to the $10 you get $10 if you make a purchase before August as well as $5 if you use the app's Alexa and Camera feature. Doesn't seem to be a minimum purchase either so you can get an item with a value of up to $25 free and clear if I didn't miss anything in the rules.
From the Rules:
In the offer period, eligible Prime customers (excluding Prime Members participating in free trial of Prime subscription) who sign in to Amazon's shopping app for the first time will receive a promotion code for $10 USD, make a purchase in the app for the first time will receive a promotion code for $10 USD, or when use camera and Alexa features in the app for the first time will receive will receive $5 USD, to use towards purchases in accordance with these terms.