Regardless of the type of paint it will likely be removed by one of the commercial strippers. Unfortunately, such a stripper may start disolving the kayak as well. Testing an area would be one approach. A second approach would just be to sand until fair and a stable surface remains. It may be that there is more than one layer of paint and that the paints are of different sorts. Flat black paint sound like it was added by a later user... likely an solvent based alkyd semigloss enamel directly off the hardware shelves.

At this age, the fiberglass is probably held together with polyester, not expoxy. You may want to consider how much work it is worth. In the end, I believe you will end up needing to paint it again when finished removing part of the finish anyway.

Hope this helps.