Since the chili bean mix that I have includes red kidney beans, and since kidney beans contain a very high amount of toxin in them, and will cause severe gastrointestinal illness if the kidney beans are not cooked long enough or hot enough to reduce the amount of toxin in them, and since the U.S. Food and Drug Administration recommends boiling for 30 minutes to ensure they reach a sufficient temperature long enough to completely destroy the toxin, and since cooking kidney beans at the lower temperature of 80 °C (176 °F), such as in a slow cooker, can increase this danger and raise the toxin concentration up to fivefold, is it known whether cooking red kidney beans in a pressure cooker will reduce the toxin level to a safe-to-eat level, and if so, how long should they cook in a pressure cooker, and is there any certain technique/method/extra steps that should be used?
I think you're conflating two different cooking methods here. Slow-cooking and pressure-cooking are two opposite ends of a spectrum, with boiling in the middle.
Slow-cooking maintains a temperature below the boiling point (100°C/212°F) for an extended period of time. Boiling occurs at, clearly, the boiing point of water. And pressure-cooking makes use of a sealed vessel to raise the vapor pressure inside, which raises the boiling point above its normal temperature and allows for higher-temperature cooking.
The FDA's recommendation relates to the temperature at which the toxin (phytohaemagglutinin) breaks down. 80°C/176°F simply isn't high enough, but the normal boiling point is. It can be safely assumed that even higher temperatures inside a pressure cooker will be sufficient to reduce the toxin to safe levels if cooked for the same amount of time.
Anecdotally, many instructions I've seen recommend a boiling time of 10 minutes (which is sometimes followed by extended slow-cooking). As with many other topics, the FDA's recommendation may be a bit conservative, but it's best to err on the side of caution.
I will comment that in my own judgment about 15 minutes at pressure is likely to be sufficient, because the temperature will spend some time above the normal boiling point as pressure builds, and will again remain above that point as the pressure falls again (especially if you're not venting the cooker, and letting the pressure release naturally). Keep in mind that a big advantage of the pressure-cooker is that it speeds up cooking, to the point where you can cook kidney beans without any pre-soak. If you are soaking, this much time in a pressure cooker will reduce the beans to mush, and you may as well simply boil for the recommended 30 minutes. If you go with a no-soaking method, it'll take at least 30 minutes under pressure (usually more like 45-50 in my experience) for the beans to cook through anyway, so you're fine from a safety standpoint.