In Flipkart product listings, whenever Delivery Charge to Buyer, is mentioned as greater than the permitted shipping rates (say Rs 30, 50, 70 for Intra-city, Zonal, National respectively), then while updating the stock via the Flipkart API, we get an error response that the shipping rate cannot be more than 30 or 45, etc. (whatever the permitted value is.) and the inventory does not update.

You need to make sure that all your products in Flipkart have the rates less than or equal to the maximum permitted values, else the inventory from Browntape will not get synced. These settings can be found under "Listings" > "My Listings" > Under an item > "Edit Selling Attributes". You will see the screen as shown below.