How can Kolmogorov complexity help me practically with measuring entropy?
How can Kolmogorov complexity be useful to you in measuring the complexity of this data?  It can't.  The Kolmogorov complexity of a sequence of bytes is not computable.

Don't read too much into that comment.  I'd take it as hinting that the idea of Kolmogorov complexity might be a relevant or interesting concept to know about, not necessarily that you can directly compute that value in a particular real-life situation.  Anyway, just because someone wrote something doesn't mean it's true.  If you're not sure what they meant by it, or you are wondering what justification they had for saying that, you might need to ask them.

I notice that Yuval Filmus's answer to the question you linked to provided a similar summary of Kolmogorov complexity, so I'm a bit confused about what is unclear here.