Hello,
This burning in calf muscles during walking can be due to a number of factors. These include muscle strain due to injury or overuse, peripheral neuropathy due to traumatic injuries, metabolic problems, infections or diabetes, spinal causes like degenerative disc disease, tumors, herniated spinal discs, spinal stenosis, peripheral vascular disease or shin splints due to inadequate warm up before and after exercising.
Apply cold compresses, do proper warm ups before and after walking and walk at a medium pace firstly. If the symptoms persist then consult a physician and get these causes ruled out.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Think it could be shint splints? These are aided by stretches. I used to have sharp calve pains after walking up the parking garage stairs. I stretch them every now and then and the pain went away.