It is the height of the chimney which will have effect on draft and not the volume of gasses within. The recommended height of a chimney is 4.5 metres.
There are many reasons why smoke can sometimes come back down the chimney, this is called ‘back syphonage’ and is affected by pressure conditions in the house.
Firstly, there must be adequate air movement in the house to make up for the air exiting through the chimney.
Do you have an air vent? If you have a stove above 5kw then you are required to have one!
An open fire demands more airflow so the same applies but the air vent needs to be correctly sized.
Secondly, there must not be too much competition from other devices in the house such as extractor fans or air exhaust systems, if something else is sucking the air out of the house, the chimney might not be able to overcome it.
And a final point would be to consider a proper chimney design, the chimney must be able to accommodate the volume and type of fumes being emitted by the appliance it serves – perhaps you need your chimney lining?