Is there a relationship between long-term use of nicotine chewing gum and venous stasis in the feet?

No: Extremely unlikely. Interesting nicotine/smoking doesn't affect the valves in veins- it is, however, a risk factor for blood clot formation. Smoking definitely causes arterial vascular disease.

Not likely: Nicotine is what makes smoking addictive and helps you to get coronary and peripheral arterial disease. Nicotine has little effect in causing chronic venous sufficiency (stasis). Unfortunately the nicotine in the chewing gum can also be addictive and it is good to get off of it but stopping it won't improve your venous stasis. If you have venous stasis, your should see a vein specialist.

Yes: Nicotine causes hypertension & often leads to peripheral vasoconstriction with constant use. You may experience cold feet & hands due to decreased circulation.