Chemistry - Why doesn't oxygen replace chlorine?

You can displace chlorine from hydrogen chloride.

With sodium chloride, if you did form sodium oxide it would be a strong base. As such it extracts a $\ce{Cl^+}$ moiety from any potential chlorine molecules. Sodium chloride is oxidized by oxygen, but the oxidized chlorine ends up as hypochlorite oxyanions such hypochlorite (i.e., oxide coordinated to chlorine).