I have spinal stenosis; can this be inherited by my kids?

Unlikely. Unlikely, but there are syndromes that are associated with smaller than average spinal canals that have a genetic basis.
No. There is a condition in which people are born with a narrow spinal canal. Most commonly occurs in the cervical spine and is termed congenital spinal stenosis. As far as i know, this condition is more of a spinal anomaly (birth defect) but not actually linked by a gene. Dr. J.