I agree with Kevin's explanation, but the word "involuntary" makes me think that it had nothing to do with real practice, but the sentence is more of a joke - rather than saying "I fell in the water 3 times," the author makes it sound more impressive.

In this case, I believe "drill" is means more something like "practice session". It's a completely different meaning than the spinning kind of drill haha :P When we're in school, we have "fire drills" which means the fire alarm goes off and we practice evacuating the building safely. Sometimes when you're on a sports team you might "drill a maneuver" meaning you're going to practice that maneuver several times. In your sentence, I'm picturing someone in a kayak that accidentally flipped over (capsized) and had to practice flipping back over.

Fire drill, emergency drill, military drill. Repetitive instruction/practice. You do capsize drill when yachting, canoeing, rowing etc. If the drill was 'rather involuntary' it was not deliberate practice. It's a nice humorous way of saying the writer fell in the water. Splash!