The "are you allowed" question is really up to Amazon; from the specs you've given, the answer seems to be "yes", and in fact from a pure megapixels view, by a long shot. 200×200 pixels is less than 1% of a megapixel, and you have 13 megapixels to work with.

But then you ask a perplexing question about "highest quality allowed". If by "quality" you simply mean "can this camera max out the file size allowed", the answer is again yes, because the 13mpix camera gives images of 4128×3096, which is obviously bigger than 2000×2000.

So why do I say "perplexing"? Well, it's because I'm concerned about the question you didn't ask about quality, which is whether your results will actually look good. This is kind of up to you (do you think they look good enough?), but also up your customers — do you want product photos that look like they were snapped with a phone camera, or do you want them to look really appealing?

You don't necessarily need a DSLR for this, but it'll give you a lot more options. In either case, what you'll need to really work with is the lighting.