[dukwon]

Δm is directly proportional to the frequency of the oscillation. (In natural units it is exactly the angular frequency: cos(Δm·t) appears in the decay rate) So indeed Δm=0 means no oscillation. You measure it by essentially counting the number of particle and antiparticle decays as a function of decay-time.

[lamontcg]

What about charged systems like proton-antiproton? We expect there to be some similarly tiny Δm there, but obviously you can't have FCNC because its no longer neutral?

[dukwon]

Protons and antiprotons must have the same mass under CPT symmetry