The measurement for gases and (gas) temperature should be taken at the same point. The sample point should be before draft diverters and barometric dampers so that the gases are not diluted and the temperature has not been decreased by the addition of outside air.
Use the following guidelines for residential or light commercial/industrial equipment.
Oil Burners / Gas Burners - at least 15 cm upstream from the furnace side of the draft regulator (diverter), and as close to the furnace breeching as possible.
For larger Equipment - downstream from, and as close as possible to, the last heat exchange device. This insures that the net temperature change (flue gas temperature minus ambient air temperature) will provide an accurate indication of the efficiency of the heat exchangers.
This question is not easy to answer due to the great differences in the equipment on the market these days and the varying uses the systems are put to. Many burners now carry out a number of purposes, being designed for one basic operation, but with the added function of producing hot water, for instance. The important facts to take into consideration are that there may be no dilution of the sample, and that there should be negligible heat loss since the last point, where useful heat is extracted from the system. Many new systems will have a measurement point already present in the flue, making life very much easier. If it is not present, then a hole will have to be bored in some way. Care must be taken with lined or other double flue pipes to preserve the integrity of the system. Judgement is needed and manufacturer's recommendations must be followed at all times to preserve the warranty on new equipment. Since measurement is compulsory in most areas, the manufacturer must make it possible to carry out measurement at some appropriate point in the system.
In almost all cases, the flue temperature will be measured at the same point as the gas sample is taken. If there are sufficient heat exchangers obstructing the stack, then the gas may be almost homogenous, but care should be taken to check the gas stream for the presence of a core of high temperature gas with a differing composition. This is the gas which should be sampled, both for pollutants and for the true flue gas temperature.
It is regrettably very common for measurements on small domestic heaters to be taken in the existing air flap. Although quick and convenient, this result will have no relation to reality. Either the sample must be taken before the flap or the flap must be held closed during measurement. Such practices are sometimes the result of prrot training but more often simple laziness on the part of the measuring personnel. These are generally trained maintenance technicians for some sort of heating equipment, and this shows a simple lack of interest in all aspects except being finished on time.