Is pure oxygen highly flammable?

A flammable material is one that burns easily.  This definition does not apply to oxygen as it does not burn at all!

A fire is created when certain substances combine with oxygen, typically accompanied by intense heat or a spark.  The presence of oxygen is required to fuel the fire –the more oxygen present, and the greater the concentration of oxygen, the more intense the fire.  However, oxygen must be combined with a fuel, a substance that readily breaks its chemical bonds to recombine with the oxygen molecules (producing a lot of heat and light).

You can prove that oxygen is not flammable with an experiment: bubble the gas through soapy water and try to ignite the bubbles.  They won’t burn because there is no appropriate fuel present (water of course, cannot catch on fire).  In the real world there is usually a suitable fuel present, thus concentrated and pressured oxygen must be handled with the appropriate safety precautions.