There should be no continuity between the armature's shaft and the commutator (the copper segments upon which the brushes ride).
There should be very close to zero ohms continuity between each segment and any/every other segment in the commutator.
However, you cannot test for shorts between commutator segments using an ohmmeter. This requires a "growler", a specialized piece of equipment that induces a magnetic field in the armature for testing purposes. Very common fifty years ago, they are all but extinct now. Note the hacksaw blade in the pic below: this truly is how this test is performed.

Personally, I haven't used one in years. If I need to have an armature checked, I have my local guy use his growler.
