Why the home inspection is not enough
General home inspections typically note that a fireplace exists and recommend further evaluation by a specialist. That is a reasonable limit on their scope, not an oversight, and it leaves the actual question unanswered.
The unanswered question is liner condition, and it is the one that carries the largest potential cost.
What to have assessed
A camera scan of the flue, the crown, cap and flashing, the firebox and smoke chamber, clearances at the mantel and hearth extension, and appliance operation on any gas or wood unit.
Ask for photographs and a written report. That document is what lets you negotiate on the basis of facts rather than an impression.
Costs worth knowing before you commit
Relining, rebuilding an above-roof section and firebox reconstruction are the significant items, and any of them can materially change what the house is worth to you.
Caps, dampers, sweeping and gas servicing are minor by comparison and rarely worth arguing over.
Timing it
Conditional periods are short. Book the inspection as early in the condition window as possible and ask for a next-business-day report so the findings arrive while you can still act on them.
If the fireplace has been decommissioned or sealed, get that confirmed in writing too. An unused flue can still leak water and carry odours into the house.