Is liquid oxygen non flammable?
Oxygen is not flammable, as it does not burn, it supports burning. For burning to happen, a strong oxidizer (for example, oxygen) and a strong reducer (for example, carbon) must be present.

No, the problem with oxygen is, that while not being flammable, it is much more efficient in supporting burning. In air oxygen is mixed with nitrogen, meaning that for the same amount of reducer a quadruple amount of oxidizer is required and a lot more heat is lost with inert gases (nitrogen). For example, iron wire can burn in oxygen, but not in air. It is also a lot easier to lit things up in oxygen. A classic experiment is to move a smoldering splinter into a vial with pure oxygen. It immediately starts to burn with a bright flame 

Now, liquid oxygen is an entirely new level of crazy. In addition to constantly releasing gaseous oxygen... If an organic material (for example, sawdust) is mixed with liquid oxygen, it becomes an explosive.