Lab126 is almost certainly not profitable since it includes most of Amazon's R&D. Drones, AI, etc. Definitely not a place to look for profits.
Kindle hardware, though, is profitable and always has been.
The K2 cost at most $185 to build (at launch) and was probably around $150 at the time of the price war.
http://ireaderreview.com/2009/04/21/...-2009-isuppli/
The K4 cost about $113 max at launch.
http://ereadertech.com/2011/10/06/ki...ost-breakdown/
Similar studies are available for newer models.
There's a reason their pricing is described as "near-cost" and not "below-cost".
Considering their market share if they really were selling at a loss the feds would already be on them.
All the teardowns and cost analysis have shown they earn $5-10 per device before any Special Offers revenue. And that is the Basic Kindle. They higher priced models make decent margins. Especially Voyage and Odyssey.