Step 1: What a chair flip changes.
A chair flip turns every axial group equatorial and every equatorial group axial. It does not change whether two groups are cis or trans.
Step 2: When the flip gives the enantiomer.
The flipped chair is the mirror image only when the molecule has no plane of symmetry. If a symmetry plane is present, the flip just gives back the same molecule.
Step 3: Test the choices.
cis-1,3 and cis-1,4 forms keep a plane of symmetry, and the trans-1,2 form also stays the same on flipping. Only cis-1,2-dimethylcyclohexane has no such plane.
Step 4: Answer.
\[ \boxed{\text{cis-1,2-dimethylcyclohexane}} \]