There is a NEW FAA rule about flying with oxygen. Please check your battery and find out what the watt hour rating is. It has to fall below the 160 maximum allowed by FAA or your battery may be banned from the flight.
The Inogen One G5 double (16 cell) battery is 188.8 watt hours. The Inogen One G5 single (8 cell) battery is 92.2 watt hours, which is under the new FAA limit. The Inogen One G4 double is 92.2 and Inogen One G4 single is 46.1 watt hours.
Zen O appears to be 97 watt hours.
The SeQual Eclipse battery is 195 watt hours. Check the watt hours on your battery or call whomever provided your equipment to find out the watt hours of your battery.
https://www.faa.gov/hazmat/packsafe/lithium-batteries