I'm a firefighter myself, just like reading smoke; creosote / chimney ash tells a story to.
Grey / brown dust build up in the stack is the best, that means all fuel products have been burnt in the stove and you have some fly ash that has stuck onto the pipe, usually when people have this build up and clean it minimal.
Black sand - slightly cooler flue gases, almost complete combustion in the stove, higher flue temps that cool off towards the top by the cap, user usually burns season wood <20% moisture content, runs the stove at cruising temps, has a good method of burning
Shiny diamonds - This is the point that something is a miss, causes: sometimes the wood is a little wet, stove is being turned down to low, chimney is outside the building envelope facing the northside of the property being exposed to cold prevailing winds, chimney is uninsulated, cap starts getting clogged spots first.
Shiny tar - caused by low flue gases, they pretty much start condensing on the chimney pretty much right away, this is the glaze that people refer to when that say get one of those sweeping logs; no clean your chimney with a brush and change your burning habits, usually the signs of this happening is constant smoke coming out the stack all through out the burn. Wet wood is primarily the culprit, its these users that run out of wet wood, find some dry stuff and throw it into the stove with out adjust there air or burning habits that have the chimney fire.
Fluffy air puff creosote: post chimney fire - if you see this, could be a lot or a little it means you have a fire in the chimney, the aftermath looks like those small fireworks kids play with called "snakes" or it looks like cheese doodles.