The Federal Aviation Administration allows you to fly with a portable oxygen concentrator (POC) if it meets these criteria:
The POC is marketed in the United States in accordance with U.S. Food and Drug Administration standards.
The POC does not emit radio signals that are detrimental to the plane.
The POC does not create compressed gas.
The POC contains no hazardous materials (with certain exceptions for the battery).
The POC has the proper labeling.
A list of POCs that meet FAA requirements is on the Transportation Security Administration website.