Thank you for reaching out to us.
Yes, it is permissible to
sit side by side on a plane while in
niddah.
There are halachic discussions of constraints on a couple traveling together in a vehicle during
niddah, but the focus is more on
romantic rides for two, or on situations in which a couple sitting next to each other would feel each other's movements (e.g., in a vehicle where the seat consists of a single cushion with some give). Neither of these concerns applies on an airline flight.
On the plane, you should be sure to keep the armrest between you down, and be careful not to lean on or touch each other. (Neck travel pillows might help prevent this from happening while sleeping.) No other special precautions need be taken.
Please let us know if we can be of further assistance.