I have been looking through lots of reviews and through their policy, and it seems like you can't. Amazon warranty is for amazon products. I think you've got to buy it directly through their website. It'd be rad if they actually write that down somewhere obvious.
Here is an excerpt from a SquareTrade forum: :.... For store-bought items, we'll need a copy of the receipt - you can also send it to us at time of purchase of warranty, and we'll keep it on file for you. " Link: https://www.squaretrade.com/merchant/laptop/features.html