Use the appraiser's numbers if you're talking about the value of the property.
You also can ask your Realtor to do a CMA--looking at the comps--and see how that figure compares with the appraiser's.
Neither the inspector nor the contractor is qualified to estimate the value of a property. The inspector will look for deficiences and may be able to offer a ballpark estimate of what it'll cost to make the repairs. The contractor will look at those same deficiences and should be able to offer a reasonably accurate estimate of what it'll cost to make the repairs.
On the other hand, the appraiser is not qualified to estimate the cost of repairs.
I'm assuming the fireplace (or the chimney) has some defect uncovered by the inspector. In that case, the most reliable figure for making the repairs would be from the contractor. However, for your own protection, get 3 estimates for the repairs. Depending on what the issue is, there may be a number of different ways to fix the defect. And even with just one method, estimates can vary greatly.
If you want the buyer to contribute to repairs, you can ask. Or let's say the repairs will cost $1,000. You can offer to pay $500 towards the repairs. Effectively, then, you'd be asking the buyer to "contribute" the other $500.
Hope that helps.