Nothing is chasing you and nowhere is on fire. Walking is read as progress under your own power, and the ground underfoot carries most of the meaning.
Walking is the quietest image in any dream dictionary and the easiest to skip past, which is exactly why it is worth separating from running and from being pursued. Nothing is after the dreamer here. The reading handed down for it is progress made under your own power and at your own speed, which is why interpreters treat a walking dream as a comment on how an ongoing effort feels rather than on whether it succeeds.
Most versions of the reading care less about the walking than about what is underfoot. A clear path taken easily is understood as a stretch where things are going roughly as expected. Mud, deep sand, snow or legs that refuse to obey are among the most widely reported dream experiences anywhere on earth, and the inherited interpretation is effort returning far less than it costs. Uphill is taken as strain willingly accepted. Downhill divides opinion, read sometimes as ease arriving at last and sometimes as a pace that has stopped being the dreamer's to set.
Company forms the second half of the picture. Walking beside somebody has long been understood as shared direction, which is why the image turns up so often in dreams about partnerships and long friendships. Walking alone can carry independence or loneliness, and dreamers almost always know which one it was even when they cannot explain how. Trailing behind somebody and never closing the gap belongs with the pursuit dreams instead, and those tend to follow a period of putting something off.
Anyone who covers several miles a day on foot is dreaming of scenery rather than of a symbol, and should read the dream accordingly. For anyone whose mobility has changed, walking freely in sleep can be one of the most moving things the night offers, and no general interpretation deserves to be laid over the top of that. Begin from what walking actually means in your life, then see whether the tradition has anything to add.


