Chronic Obstructive Pulmonary Disease is a concern for using high-flow O2 (typically 10-15 liters per minute via non-rebreather mask), but it's not a flat-out contraindication for oxygen use, at least in Washington.
The problem you encounter has to do with respiratory drive. Most healthy people rely on CO2 levels in their blood to tell their brain when it's time to breathe... you get high CO2 levels, your brain ups your respiratory drive unconciously, and you compensate without thinking about it by breathing heavier and/or faster, or yawning. The secondary indicator your brain uses to determine if you need to breathe is O2 levels in the blood... when these drop, your brain says it's time to breathe.
If you've got a COPD patient
and it's ended up making them a CO2 retainer (meaning that they've got elevated levels of CO2 in their blood all the time), the brain essentially stops paying attention to the CO2 level, since it's ALWAYS high, and relies solely on the O2 level to determine if it's time to breathe. O2 levels in your blood take longer to react to a change in oxygen availability than CO2 levels do. Since COPD patients frequently have an SpO2 around 90% (88-93% is pretty common) even on 2 liters per minute via nasal cannula, their brain is used to it being at that level, which is a lot lower than a healthy person would have (96% and up). If you put them on high-flow O2, you could easily spike that percentage back up into the high 90s... and in the process, tell their brain that they
don't need to breathe, knocking out their respiratory drive and stopping their breathing. Once their bodies use up that oxygen you got into their blood stream 30 seconds or more ago, that SpO2 can drop really, really fast (as they haven't been breathing for the last half minute), and the really sick ones aren't reliably able to start breathing again at that point.
We were trained to keep 'em on minimal amounts of oxygen, usually no more than 2-6 LPM via NC... many COPD patients are on 2-3, anyways. If you've got to stick someone with COPD on high-flow for some reason, have a bag-valve-mask nearby, because you might have to start bagging them to replace their stopped breathing. Conscious patients hate it when you do this.
It's a pretty weird feeling, actually... try not breathing, relaxing, and having someone breathe for you with a BVM. Weird sensation.