The question is, how do you know the chain is false?
A mixture of experimental falsification and better theories. We know that rain dances don't cause rain because we know what does. We can also do them 20 times on days where no rain is projected and notice that - surprise - it doesn't start raining.
We do know that certain types of meditation, for example, do cause measurable changes in brain waves. We also know that this has nothing to do with Shiva or your guardian angel whatever the esoteric explanation may be, because the results remain the same if someone who doesn't believe in that simply follows the steps.
We know that certain substances cause certain effects, but not because of nature spirits or the shaman humming over them while slowly stirring them in a pot over a fire of elm wood that was quenched with baby blood because we know which chemicals are responsible for the effect.
And yes, science does discover that its theory was wrong every now and then, but there's one important detail that all the anti-science fanatics always conveniently forget to mention: When science throws out a theory as "wrong", what it really means is "it only had a 99% match with reality, and now we have a better theory with a 99.9% match".
Newton's laws are "wrong" by todays scientific standards, but for anything that's not rocket science or quantum physics, it's still very useable because it's close enough.
So when you say "even science is sometimes wrong" then strictly speaking yes, but not in the same sense that, say, your navigation system leading you to the wrong city because it had the same name was wrong. More like the GPS being miscalibrated and you arrive at Bullshit Avenue 11 instead of Bullshit Avenue 13 like you wanted to. Yeah, it's technically speaking wrong, but it's a totally different kind of wrong than Homeopathy or Astrology.
modern Western medicine for example has no way to relate to theories of Chi flow,
Funny that you should mention that. As a martial artist, I've done some reading on that and in fact there are a couple of books attempting to do exactly that, including a spinal nerve path theory to explain some pressure point attacks and several scientific studies on meridians (all of which except one chinese one sponsored by some accupuncture society coming to the conclusion that no such thing exists).
When an esoteric system makes predictions, it can be tested. You don't even have to bother discussing its system or theories at all, you can go straight to testing the predictions.
I think the main mistake that the various anti-science conspiracy theories make is assuming that scientists hate challenges to their world-view as much as they themselves do. Religious and esoteric people loathe criticism. Scientists think differently, because nobody has ever gotten a noble price for confirming an established theory for the 50th time. But proving it wrong - that's a good start.
There is bias in science - Kuhn was right about paradigm changes. But it's not a directed bias the way a conspiracy theory presumes.
So yes, if you can repeatedly create a phenomenon that science cannot explain, you will almost certainly find scientists quite interested. In fact, Randis million dollar challenge still awaits a taker, so there's money on the table.