Don't forget the obvious: keep oxygen away from fuel, and keep flame away from both. And keep attention on the airplane if/when you're fiddling with oxygen supplies.
Also, when you talk with your dad's physician, keep in mind that some people with COPD or similar conditions will have a different "normal" pulse oximetry reading, often as low as 88-92%, compared to normal (usually >95%). That's because while most of us use "too much CO2" as our body's signal to breathe, many people with COPD chronically have too much CO2, so they instead use "too little oxygen" as their signal (the so-called hypoxic drive).
So, if you do decide to use a pulse oximeter to guide your father's oxygen therapy, talk with his physician about what "his normal" is, and don't necessarily crank the O2 to get him up to 98% like you might with the average pilot.
There are formulae and tests that can be used to deduce how much oxygen will be needed aloft, but in all likelihood for a couple of 15-minute flights at 3,000 feet, your father's physician will just recommend turning the O2 up a bit if dad feels uncomfortable and landing if he still feels uncomfortable.
All that said, I've never met your father or reviewed his medical information, and this is not medical advice.