It is rather a structural (not mechanical) problem.
What's important here is not the boiler capacity or how the furnace is fired but the structural properties of the chimney itself and how it is attached to the boiler.
Notably, an engineer would need to know pipe diameter, wall thickness (I mean structural steel only; not liner or other materials) and the desired height.
The base attachment detail should be evaluated and reinforced by ribs and/or a skirt if local buckling problem or tearing (prying) or the bolts/welds occurs.
It is imperative to realize the nature and magnitude of the lateral loads: wind loads (if the boiler is outside), dynamic impact during transportation (if the boiler is going to be transported) and other (if any)
If the chimney pipe of a given diameter and wall thickness cannot withstand lateral loads (in combination with its self-weight) you can do one of the following:
1. increase its diameter (increasing wall thickness would not be as effective unless you have local buckling problem),
2. attach guy-wires
3. reinforce it with vertical elements (like angles or plate ribs) continuously attached along the pipe.
You have to specify the local area & regulations.Sulphur % in FO ?Seismic data of local area.
In normal conditions 750mm dia x30mtr hieght,10mtr flair section with base dia of 1500mm is ok.The detail design conforming chimney's safety for bending & deflection will depend on above basic data.