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According to the website of the Andaman and Nicobar government, you will be able to receive the Restricted Area Permit on arrival at Port Blair Airport. The website also mentions that you'll be able to apply for the permit at all Indian missions abroad.
While I would assume that you will be able to board your flight to Port Blair from Kolkata without any problems, if you really wish to have this itinerary foolproof and account for checking staff error, you may consider applying for the permit at an Indian mission before arriving in India. Whether you have flights to Port Blair on one itinerary or separate ones does not matter in either the case of applying before or recieving it on arrival.