In general, try to place chairs up higher in the load to keep weight off of them. Ensure they are wrapped to avoid abrasion.
Chairs can be problematic when they have a sloping back, making them difficult to fit in nicely between boxes. Avoid forcing the backs into upright positions when this causes force to be exerted only on the front or back legs.
Swiveling desk chairs present additional challenges. Not only are they oddly shaped, but their wheels will suffer damage if heavy weight is loaded on top of them. Some desk chairs can have their rolling assemblies removed, making two smaller objects that can be more easily loaded.