The buyer will likely hire a chimney professional to inspect the chimney as part of their due diligence in the inspection process. It’s quite possible that beyond having your chimney cleaned from time to time, you’ve done very little maintenance. And in many older homes, the chimneys have deteriorated. It’s a good idea to pre-inspect your chimney to see what they will find.

With regard to the furnace flue, if it’s found that it needs to be re-lined understand that this will come up as a safety consideration in the inspection. It’s much harder for the seller to decline to repair or give credits for things labeled as safety issues.