During Audible's early years it would frequently offer discounts or bundles that combined an MP3 player and an Audible subscription.
Those bundle offers petered out over the years, although Amazon has offered a new one every once in a while. In their latest offer, you can get a free basic Kindle with the purchase of a 1-year Audible membership. The device in question is not as good as the Paperwhite, but it does have Bluetooth and supports audiobooks.
The way it works is that you visit the offer page on the Audible website, click the button to subscribe to Audible for one year at $130 ($20 off the regular annual price). After the order is processed, you’ll get a credit of $80 you can apply toward a Kindle.
The offer is good until 4 May, and it is open to new customers only.