I'm a Health Professions Council registered graduate podiatrist, you can buy chillblain ointment/cream which seems to soothe them for some people but as there mainly antiseptic really it's probably placebo effect. But if it stops the itching I wouldnt care personally.
The blood supply to the feet isnt always equal, one artery system can be quite clogged with fat and the other can be relatively clear. We were taught the body is essentially two halves jointed together more than a whole.
We dont see many chilblains anymore, central heating prevents a lot of them but if you dont put your heating on when it's cold and then put a hot water bottle on them or an electrical device eg electric blanket or heated foot warmer then the change from cold to hot will damage the circulation and cause a chilblain. Avoid smoking, people always think smoking only affects the lungs but it reduces blood supply to the legs and feet and most patients I have with periphearl vascular disease are either smokers or ex-smokers.
Try thermal longjohns (dont laugh I wear them and I'm only 34), thermal socks and thermal liners in your shoes and slippers.
When your feet are cold avoid any direct heat to them eg footbaths, putting them near the fire/radiators, hot water bottles or anything that gives out heat.
Instead put the heating on, leave your thermal socks on and if possible raise the feet to hip level eg put them on a foot stool or lay on a sofa and put a duvet over them to warm them slowly. Never scratch them, they can rupture and because the blood supply is poor it can take weeks to heal them again.