The Gran Canaria boat fishing license is valid on all of the Canaries, and is ideal for those who want to do trolling. If you don't want to do trolling, then the regular shore fishing license will do, even if you're fishing from a boat. In the video below, you can see one of the locals fishing with his kayak.
Below is the order form for the "fishing from a boat" license, with trolling. The cost of this type of license is 70 euros, but you can save a few euros, if you order more than one license. The maximum processing time is a week.