To some extent, Flipkart.com:India::Amazon.com:USA is more accurate than Amazon.in:India::Amazon.com:USA.
Amazon.in is following a purely marketplace model i.e. only 3rd party sellers (which is unlike the Amazon we know in US). Whereas Flipkart has a large percentage of stuff offered by 'WS Retail', which is essentially Flikart itself.
Technically Flipkart isn't a Indian company as Flipkart is registered in SG. But since all its operations are in India you could say it serves India. Just like amazon.in which serves India.
WS Retail is now a separate entity not run by Flipkart anymore. It was sold last year.
This was mainly to bypass the FDI laws. So WS Retail is like a wholesaler.
So WS Retail is a seller technically. Also you cannot say they run on different models, Flipkart does have more than a one seller so the model is still the same as amazon. Flipkart just eats other sellers at times with the WS Retailer's discounts and stuff. Just like amazon?
If every legal aspect is off the table then Flipkart is running WS Retail and other sellers are at mercy of Flipkart's(WS Retail) listing price.
Also Amazon.in sellers are all Indian (brick and mortar stores)sellers, so theres that.
I'm aware of the stuff they are pulling to escape the Enforcement Directorate & foreign investment related laws. Still, from a perception point of view, I feel, as of now, they are the "Amazon of India" more than Amazon.in themselves.
Amazon.in is following a purely marketplace model i.e. only 3rd party sellers (which is unlike the Amazon we know in US). Whereas Flipkart has a large percentage of stuff offered by 'WS Retail', which is essentially Flikart itself.