@MacSparky, since this was probably off topic for the episode that it appeared in, here is my experience.
Many fountain pen owners worry that fountain pens could burp out ink when the cabin pressure is reduced. This would end up inside the cap, get on the section and then when you try to write with the pen you get inky fingers. In fact, the first time I experienced this was with a Pilot V5, so it’s not just fountain pens that suffer. The root cause is that air inside the pen expands more than the ink, so can cause ink to be pushed out. Many people recommend to either fill the pen completely before flight or empty the pen completely before flight.
If you have more than one fountain pen, you may know that with some, the nib dries out faster. There may still be ink in the pen, but it won’t write until you dip it in water as a minimum. I reasoned that this was because the liquid in the ink was evaporating out through the cap seal. So for flying with pens, I choose the ones that don’t dry out.
In practice, I find snap caps and slip caps dry out fastest, finely machined Kaweco Al-Sports don’t. A Platinum 3776 has a good air seal, so does an Esterbrook Estie.
The first time I flew with fountain pens, I carefully wrapped the chosen few in tissue and elastic bands, then a ziploc, put that in my Nock Sinclair and when on the plane I kept the Nock Sinclair upright in the seat back pocket, making very sure not to leave it there upon landing. However, when nothing bad happened, nowadays I just pack them in the Nock Sinclair and keep it in my bag. The worst I ever saw was a bit of ink coming out on a nib the next time I used the pen.
It goes without saying, don’t take the cap off a fountain pen during flight. When you open the pen after landing, check the section with a bit of tissue paper before use.
Hope this helps, and fly safe!