If your burner already has a chimney, just measure its outside base diameter, then compare it to those available on my CHIMNEYS page.
If you do not have a chimney to measure, use the "paper chimney" method:
Use a sheet of firm paper, like a magazine cover, and roll it into a tube so it fits into the burner where the chimney rests. Let it unfurl so that it fits snugly in the burner. Tape the loose edge. The tape prevents it from unfurling when you remove it. Remove it from the burner and measure its diameter and compare it to the CHIMNEYS shown.

HEIGHT
The height of a chimney has very little effect on the efficiency of most ribbon and cord wick burners, unless situated at elevations above 6,000 ft. (2000 m.). For example, the flame will burn properly whether you use an 8.5" tall chimney versus a 12" tall chimney. Pick a height that you prefer for the appearance you like.
If your burner has a tubular shaped wick, such as a Kosmos burner, then you should select a Kosmos chimney. These are specially designed to provide the cleanest & brightest flame.
If your burner has a stitched tubular shape, such as those used in Central Draft burners (Miller, B&H, Rayo, Royal, etc.) then a chimney no shorter than ten inches works best.

SHAPE OR STYLE
This characteristic varies to provide people a choice to suit their taste. It will not appreciably affect the flame, with one exception. Kosmos burners should be fitted with Kosmos chimneys only. All other kinds of chimneys: beaded top, big bulge, slim bulge, plain top, crimp top just change the appearance of your lamp, not the efficiency. If you would like the lamp to be historically accurate, email me a small picture of your lamp and I will make a recommendation, but Read This before you do so.