If you are referring to the cash flow statement, which I think you are, there are no "weird non-GAAP claims" involved.

Their latest 10Q shows GAAP pretax income of $1.9 billion.

If you're referring to total change in cash which was -$4.2 billion, that's because they reduced their accounts payable by $10.2 billion from paying all the suppliers after the holiday season. Looking at the consolidated statement of cash flows of a seasonal business very, very easily leads to misunderstanding the business.

Operating cash flow was $18 billion for the year ending 3/31.

I'm talking on a yearly basis, not a quarterly basis. Due to the seasonal nature of their business, I'm sure the quarterly numbers are more choppy. I think the general point, that they've been able to self-finance this enormous growth (save for some certain real estate purchases or acquisitions), stands.

Free cash flow is a non-GAAP metric. Amazon provides three different free cash flow calculations (depending on how leases are accounted for). In 2015-2017 the corresponding figures are $26.4bn (7.5+10.5+8.4), $14.8bn (4.9+6.5+3.4) and $5.8bn (2.6+4.7-1.5).