No, Amazon/Flipkart arranges the courier themselves mostly. Here Amazon usually sends ATS (Amazon Transportation Services) guy and Flipkart uses
Ekart logistics and Myntra uses Delhivery for pickup. These are their own courier services or service they have tied up largely who check the product is in intact condition or not. They come with pick up recipt as a confirmation and give it to us while taking the parcel.
I also read in several online blogs where they have said usually at smaller towns and villages where they don't operate themselves they ask people to arrange a third party courier and send it themselves attaching some return receipt paper outside of the box and share tracking number after which they initiate refund with courier charges.
Their own pickup is hassle free. These days many couriers like Bluedart, Delhivery providing their pickup service for our own bookings too. So book for a parcel pickup online, courier guy will come and take it from home itself.