How dangerous is breathing in bad smells?

I was at security at an airport and it smelled pretty bad and was wondering if that can affect or damage the body in any permanent way.

It depends on what the cause of the bad smell is. Smelling a bad chemical might cause you harm; smelling someone's dirty feet won't.

I walked outside and could smell a factory burning off chemicals and I feel fine.

Bad smells by themselves are fine. If the smell comes from something toxic then that is a concern in the long run. Even toxic items may not have a smell though so smell by itself is not a good indicator or anything.

Bad smells, or 'miasmas' are responsible for diseases. Second hand smoke for example.

That is why substances that remove bad smells, such as essential oils work to stop disease, and substances like vaccines which ignore them do not.

Well, I breathe in pot and k2 all day and I'm fine

I'm assuming you are referring to body odour. It is not dangerous. There are some people traveling whose sanitation and hygiene is not where it should be.