Quoting , ORGANIC CHEMISTRY second edition by JOSEPH M. HORNBACK, UNIVERSITY OF DENVER
1,2-dimethylcyclohexane has two chirality centers.
The cis-diastereomer has a plane of symmetry bisecting the ring bond between
the two methyl groups and therefore a meso compound.It is not chiral and does not rotate plane-polarized light.The trans-diastereomer exists as a pair of enantiomers.
The chair conformation of cis-1,2-dimethylcyclohexane shows that it is chiral.
But due to ring-flip , another conformation ,its enantiomer of the original conformation is also formed.These conformers interconvert rapidly at room temperature, therefore cis-1,2-dimethylcyclohexane is not chiral.
Further I quote
"stereochemical analyses such as the preceding one can be done with drawings using planar rings" pg.235.
A molecule cannot be optically active if its chiral conformations are in
equilibrium with their mirror images. We consider such a molecule to
be achiral. PG- 193 - ORGANIC CHEMISTRY .EIGHTH EDITION
L.G. WADE , JR . WHITMAN COLLEGE