I take it back, the charcoal kiln literally says Carbon. Now I just need to figure out if I can place it in the city/on my roof

No worries, I did have another idea or two for other methods of getting Carbon, but so far it's limited to burning farmed plants.

You should def add some sort of advanced carbon making building that burns plants faster. Also, what are the current burn times per plant to make 1 carbon?

I have set the kilns to use 'output per day' - and in typical Kenshi hemp-loving fashion, it burns faster than other plants. Hemp has a 12 production multiplier and other plants have 8 - which presumably means 8 and 12 per day, meaning 1 every 3 or 2 hours respectively.
I haven't specifically measured the time it takes to cook charcoal, so I'm not sure how well the modding tooltips actually translate to the real experience.
But I'll definitely be adding some extra bits for carbon and fuel soon.