The home is so old there is no central air system... furnace would be new, duct work new...

They ran some of the ductwork in the basement, which has an unfinished ceiling, between the floor joists - maybe you could do that?

“Because the $20,000 took so much away from their equity to put into another home, they decided not to sell,” she said.Another client of Chaname had difficulty selling his home because would-be buyers balked at paying $16,000 more for a home with HERO-financed air conditioning, duct work, water heater and insulation when similar homes were selling for less.The buyers argued they were paying for the improvements twice – through the higher valuation on the house and assumption of the loan.

Its likely from all the standing water that it has started to rust out the duct work in the basement or grow mold inside it/throughout it (even on the upper level floors).Saw that recently on a property I looked at with 5 feet of water in the basement from when the sump pump backed up and overflowed (bank turned the electric off 3 years ago).

Since it already has the ductwork, it could be replaced with a forced hot air furnace. 

If you currently have a forced air furnace in the duplex, an a/c unit may not be too expensive, and probably won't require any additional duct work, assuming the furnace is relatively new and a compatible a/c unit is available. 

We have a quote of $385 to have this replaced with proper duct work."

If I could add to what John Leavelle said  ; it could cost as much as $60,000 to do a full Rehab here in the Philadelphia Area        My Friend Sean just did a Rehab in the Port Richmond Area Close to Fishtown and he it was $60,000        Sean has done many flips and I thought he went as "Budget" as you possibly can , for an example ; he paid $7,000 for a brand new HVAC  (Heat & Air Conditioning)  with new duct work , where that would have been double in the open retail market       Good luck with the project & feel free to reach out to me if you need any help or have questions SincerelyRick      

So don't overlook that you could get some of the high velocity stuff for some areas if you already have duct work in limited spaces.

Unless it is an older home (ie radiant heat and no duct work) I would add it if at all possible.