I want to learn how to manipulate a balisong (butterfly) knife, for defense, and for cool factor. What’s the best way to learn?

Never, never, NEVER use a live (sharp!) weapon for practice, unless and until you are already approaching full competence with the practice instrument, and have someone on hand to render first aid should it become necessary. Instead, use a well-balanced substitute that simulates the live weapon as closely as possible when practicing.
As answered earlier, the balisong is not generally regarded as a first-tier self-defense weapon. Firstly, it takes some time to deploy, time you may not have. Secondly, it’s fiddly – the more complex a weapon is to deploy and utilize, the more ways it can fail you when facility matters most.
Balisongs only lock the blade when fully closed, making it more likely to bite *you* during transitions. It only takes an unanticipated or unnoticed half-turn on the longitudinal axis of the knife to give you a very bad day (and as-designed, many balisong knives don’t have a clear “tactile” indication *on the hilt* of which side of the knife is sharp). The functional loss of your dominant hand during combat is a non-trivial risk.
Thirdly, in the West at least, it’s difficult to explain to a jury that you weren’t carrying it with “intent to go armed”, as the balisong doesn’t have a particular non-combat practical application that wouldn’t be better served with a simple penknife, and might be judged by the judge/jurist as “intimidating”.
Most importantly, knives in general aren’t great “self-defense” weapons. Prized on the battlefield, they have a multitude of devastating *offensive* applications, but fewer solid defensive ones. Unless your intent is to kill your attacker, there are better melee options.

Smith & Wesson Extreme Ops SWA24S 7.1in S.S. Folding Knife with 3.1in