There are, as of now, no licenses or permits that you'd have to obtain merely to set up a social-media platform. You may decide on the business entity through which your platform is to be run (a company/partnership/llp/independent propritorship etc.), once that is done you may register/incorporate yourself as a company/llp etc., as the case maybe. You may register for a trademark for your platform's name and logo (this can be done after your business is operational as well). You may obtain a PAN, TAN, GST registration etc. If you believe you are working towards innovation, development or improvement of processes or services or that your business model is scalable and has high potential for employment generation or wealth creation (as provided under the Ministry of Commerce & Industries Notification No. GSR 127(E)), you may register yourself as a start-up (this will entitle you to certain tax benefits).