The most common deficiency that could cause a burning feet sensation is vitamin B12 as a lack of it causes damage to the myelin sheath around the nerves. However, this is a very uncommon cause and is unlikely to be the cause of burning feet in Western countries. Oddly, Vitamin B12 is widely recommended in western countries to treat burning feet … go figure. Just ask those with burning feet how Vitamin B12 supplements worked out for them.
Burning feet has a number of causes and you really need to consider the common ones first rather than look for a deficiency of things like vitamin B12.