Maybe I´m completely off here, but let me consult
Wikipedia.
A natural draft smokestacks throughput can be calculated by this formula:
Q(m³/s)=cA sqrt(2g h ((Ti-To)/To)).
Assuming an area (A) of 4m², c of 0,65 (Wikipedia claims this to be realistic), g of 9,81m/s², an internal temperature of the smokestack of 100°C= 376 K (Ti), an outside air temperature of 25°C = 301 K and a height of 100m (h), there will be a mass flow of 81m³/s, divided by the area, this means a velocity of 20m/s. And with an air density of 1,293 kg/m³, this is 105kg/s. For simplification, I assume pure air here, which is of course daring for a smokestack.
Now let us add a jet engine to the top of the smokestack, drawing external air for its combustion and discharging via some kind of mixer nozzle right at the top of the smokestack.
A RR Avon as used in the Comet for example is said to put out 104kg/s at 360m/s.
p = m v.
Therefore, 104kg/s times 360m/s = 37440 (for the Avon), and 105kg/s times 81m/s = 8505 (for the smokestack).
Summed up, this leaves us with a total impulse of 45945 kgm/s², divided by the total mass flow of 209 kg/s, this will give a velocity of the exhaust of 220 m/s.
Compared to the original 49m/s before the addition of the Avon, this is quite a difference, I think. However, how high the exhaust plume will rise before this additional velocity has been eaten up by assorted eddies is beyond my humble means of calculation.