I'm wondering if instead of purchasing a SLR, if I can't just use my Samsung Galaxy Note 3 camera instead. This is for eCommerce photos; women's clothing, tops and bottoms namely and some jewelry. Amazon requires the file size to be 10MB, 72 pixels per inch, 200x200 to 2000 x 2000 dimensions and ratio 5:1 or 2:1 or 1:1. The Note 3 cam has these options: 4:3 13M, 16:9 9.6M, 4:38M, 16:9 6M, 16:92.4M. Can I use one of these options on Note 3 to submit highest quality allowed on Amazon? Thank you!
Product photography depends on creating a flatteringly accurate image of what you're selling. That goes far beyond filling the permissible pixels on your host site.
Accurate colour reproduction is very difficult to control with a camera that doesn't let you process raw files or set the correct white balance; an SLR or advanced compact camera can do that.
The wide-angle lenses of cell phone (and tablet) cameras will exaggerate the effects of distance: something close to the lens will look much larger than things that are father away. This is a problem for anything that isn't laid out flat and parallel to the camera, especially for three-dimensional products such as jewellery. Using a camera with a zoom lens, such as the kit lens that's included with most DSLRs, lets you control perspective and choose how you want your items presented.
So yes, you can use your Note to take the photos, but you'll still need to downsize them (and crop, as desired) before they can be uploaded. Using an SLR, however, will give you better results.
The lack of raw support and limited dynamic range of the smartphone camera is going to make getting proper light box exposure of the products far more time consuming and difficult than using even a basic DSLR, let alone a good one.
Technically, with sufficient effort you could probably make a passable image with your Note's camera, but I personally wouldn't want to go through the aggravation and trouble it would be, particularly when the actual image quality likely still won't be near that of a decent DSLR.
Also, you will certainly need proper lighting and probably a soft box to get the lighting right. Unless you want to use continuous power lights, having the ability to sync with multiple flashes would also be helpful, though continuous power lighting is also an option.
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.