Quik-Crete doesn't have the operating temp range required to meet code in most places. What you're looking for is a
refractory cement. (Some box stores and some hardware store will carry it.)
But before you just patch it do a more serious flue inspection- jadnashua tells it true. Oil fired exhaust condensate is the worst offender, but gas-fired exhaust condensate is still enough to etch away all of the lime, leading to flue-penetrations and structrual instability if left unchecked.
The dew point of the exhaust in the flue is determined by two operating conditions- the temperature of water returning to the boiler from the radiators/baseboards, etc, and the amount of dilution air introduced into the exhaust after it leaves the boiler with either draft-hoods, or barometric dampers. For oil-fired boilers you should NEVER go below 140F as the average return water temp as it's standard operating mode, 130-135F may be OK for gas burners, provided the chimney isn't oversized. Barometric dampers can (and need to be) adjusted to ensure sufficient dilution air, but draft hoods are pretty much opimized by design. The cross sectional area and height of the chimney should be properly sized for the BTU rating of the burner(s). There is some wiggle-room there, but going with the smallest recomended size for the burner rating is the best from a condensate potential and overall efficiency point of view. A 5x oversized flue drafts too slowly an presents a much larger surface area to the flue gases, increasing the condensing potential. A narrower flue will draft faster, and will warm up during a burn, re-evaporating any surface condensation that might have occured at the beginning of a burn.
When a gas water heater is sharing a flue with a heating appliance, the flue is almost always at least 5x oversized for the water heater alone, even when right-sized for the combined BTUs of both burners. In practice this is usually only problem if the heating appliance is permanently removed, but over a decade or so the water heater's condensation can destroy the chimney. (google "orphaned water heater" for lots of techical detail.)
Job-1 is to look at the BTU rating of the burner(s), and measure the size of the flue liner (usually most easily done at the top), and the height of the chimney to see if they're even remotely compatible:
Ideally you'd want the burner to be at least half the max-allowable for a liner-size & length. The above chart is for round liners- multiply by 1.25 to come up with the approximate rating for a square flue. Do the math on a square flue to figure out your cross-section factors for a rectangle.
In the process of measuring, hopefully you won't come across anything that looks as spalled & eroded as this:
Look for things like loose brick or missing mortar, broken/spalled liner around the top of the chimney too, since that's where the flue gases are coldest, and most likely to have condensation issues.
It can be expensive, but sometimes the right thing to do with an oversized chimney is to install a stainless liner right-sized for the burner as part of your chimney repair.