WRT to the size of the system, is the current system keeping the house cool enough? That would tell you if you need another ton.

How many rooms do you have? How do you heat?

If you've ever seen Mike Holmes on his show "Make it Right" he will tell you that duct for heating (or anything else) should NOT be run through a chimney. In most places, it's illegal, as it's so unsafe. If you're not comfortable with your estimate, call another company for an estimate. As I've seen, most homes built in 60"s and 70"s are not equipped with a furnace that puts out enough BTU for adequate heating for the square footage. Finding flex tubing in your heating runs, could also be a "repair" from a homeowner who has no idea what they're doing or have not thought of the consequences of using substandard materials. Again, it could also be illegal to have used it. Make a few calls, ask what is the standard BTU raing for your square footage. And what are the laws for flex tubing as duct line runs. Research your furnace online before you decide. Doing a little research online and calling HVAC companies may put you in a more informed place to make your decisions. Good luck!

Thanks for the follow ups! The current system is 4 ton, but it doesn't quite cool the rooms at the farthest ends of the run upstairs very well. I think 5 ton makes sense. Not sure about a 3 ton upstairs / 2 ton downstairs split. Also, we are in Charlotte, NC and the house has 6 rooms down including one bathrooms and 6 rooms up including 2 bathrooms. Heat would be through a gas furnace downstairs, but gotten some suggestions for a heat pump upstairs.

Sounds like new systems up and down to avoid chimney might be needed. (Not sure how it will be afforded though!)

I asked about the performance of the current system because if it is adequate, the 4 ton would certainly be adequate. Since it is not, there is no way to tell if it is not doing the job because it is too small, or because there are other problems like duct leaks or inadequate ducts to the furthest ends of the upstairs runs. Insist on a full evaluation of the system including a physical inspection of the duct system, heat transfer calculations, and the adequacy of the size of the ducts for each room. You should see reference to "manual M' and 'manual D"

Ducts outside of the house envelope are particularly problematic because duct leakage turns your HVAC system into a power vent. Even with very good ducts there is leakage and then there are room to room pressure differentials to deal with that can do the same thing. That is why Jackfre suggested mini-splits. That will be pretty costly for 12 rooms. Heat pumps will also be more costly to operate than gas furnaces in the current situation.

I have learned on this board that in some areas the current building code requires a system for each floor in a home. That should tell you something about the difficult of heating and cooling two floors with one system. One of the most common complaints you see posted here is a big differential between upstairs and downstairs. To get heating and cooling right, you really have to move dampers when switching from one mode to another. There is just no way around the fact that you need more air flow upstairs in the summer than in the winter.

For those that don't like the idea of a duct in the chimney, I understand that you would not want a duct in a working chimney. Is there any big problem with re-tasking a disused chimney for a duct chase?

Thanks ionized. Unfortunately, closing the dampers downstairs is what called our attention to the problem initially. About a week after doing that, we started to get a terrible moldy smell in the house and checked out the crawlspace to find tons of moisture, fallen insulation from the ducts and mold on the joists. This will be another project to tackle, which is increasing my desire to go cheap on the HVAC.

A couple additional questions following more research:
1. Has anyone ever used aeroseal? I'm wondering if this could be used to ensure a good seal on the chase in the chimney so we can still use one system.
2. How well does zoning work? we've received a suggestion to do an upstairs and downstairs zone, rather than installing 2 new systems.
3. How subjective are the manual J/M?etc. tests? We've had multiple people that have spent a lot of time measuring rooms, windows, etc., but some have come back suggesting a 4 ton system and some have suggested 5 ton. If you are in between, is the general rule to round up or down?