Thanks for the mention, Penguin. Here are a couple of those flags that I used to teach my students.
1) As you point out, it’s very difficult to prove the factual claims in a conspiracy theory are false. But it is often easy to prove that the inferences are false. If we label the two premises of an argument “P” and “if P then Q”, you have to do research to disprove the P, but it’s often easy to attack the “if P then Q”. Erich von Daniken says “if the Egyptians have embalming techniques far more advanced than ours, they must’ve learned them from space aliens.” He may be right about the embalming techniques, but his inference is bad. It’s easily dismissed by pointing out that they had more incentive to get good at embalming because of their religious beliefs.
2) Most conspiracy theories rely heavily on the argument from ignorance. This is a form of the logical fallacy called affirming the consequent. The stock example is “if this chair had an invisible cat in it, it would appear empty. this chair appears empty, therefore it has an invisible cat in it.” CS Lewis describes this argument as “the fact that there is no smoke is proof that the fire has been carefully hidden.” Conspiracy theorists really do argue this way. When I asked someone about evidence for their claim that Hillary Clinton had committed several murders, they replied “of course she didn’t leave any evidence. She’s far too clever for that!”