There are a few different respirometry methods you could follow; it depends what exactly you need from these measurements. Flow-through is typically more expensive but also more stable and reliable than closed box at the scale of an individual fly. In any case it is likely to be relatively expensive to set up, as to achieve good discrimination between treatment groups or individuals, and because the animals output such a small volume of CO2, the CO2 analyser precision must be high. Fortunately, D. melanogaster have a respiratory quotient of ~1 so you do not need to also measure O2 production to accurately calculate metabolic rate. You only need a stable baseline reading and then a measure of CO2 production to estimate metabolic rate at rest, but you might be limited to the higher end of Sable Systems or Li-Cor instruments in order to reliably detect a difference between baseline and animal CO2 rates.
Some examples of Drosophila respirometry:
Berrigan and Partridge (1997) used a flow-through respirometry on individuals using a combination of Sable and Li-Cor instruments.
For now, my conclusion is that I don't need to do this as urgently as I thought and I'll worry about it if it seems to become important again. But it is a general interest, so it will be good to know how practical it is.