If someone wants to just paddle with friends and family, and not doing any business then there is no need to get any type of License. At the same time please wear pfd and carry equipments like (mobile phone in dry bag, emergency light, water for hydration). Also make sure that the water body is open for public usage like fishing.
If you want to start your own kayaking Business in India. Here is the step by step process
Once you have the above document ready approach the District Tourism Office which is mostly located inside the District Collectors office.
Prepare a project plan of your kayaking route and submit it with all the document
If you need help with preparing project or regarding NOC you can contact me directly on phone +91-8722846295