In the treatment of patients with deep vein clots (DVT) it is recommended that they wear stockings 365 days a year to prevent additional or recurrent DVT and pot thrombotic syndrome. I wear stockings 23/7/365 and some people should do the same. Read the book about post thrombotic syndrome on the link below.
Compression stockings are actually used to treat patients who are at high risk of deep vein thrombosis. The compression aids venous return and decreases the risk of clot formation.
There is no risk of DVT. If, however, you have superficial venous insufficiency and wearing stocking of pressure lower than needed, there is a definiteve risk of thrombophlebitis.
Compression hose function by compressing the calf muscles and thigh muscles (if thigh high) to push the blood out of the veins to increase the venous return to the heart and decrease the venous pressure. Blood clots when there is decrease movement of blood (stasis), trauma to a vein or increased clotting (hyper coagulable). Usually there is no need to wear compression hose 24/7 but wearing them should not increase your chances of DVT but rather decrease it since you are reducing venous stasis and increasing the venous return.