Your question is similar to this bicycles.SE question.
Estimating aerodynamic drag can be tricky, but can be done with field tests. If you can find a quiet road that is protected from the wind and you have a way to record speed each second, you can do coast down runs to determine the drag with and without the flag. The approach is discussed on page 108 here. You do need a recording device to capture speed each second, but nowadays many riders use bike computers with this feature. If you have a device such as this and a speed sensor on your bike, you need no other special equipment.
Details are provided in the link but, in summary, you will want to do at least two runs starting at different speeds, then solve for the two unknowns of CdA (drag area) and Crr (coefficient of rolling resistance) given that the road surface and road profile are the same for both runs. Since your Crr should remain constant across runs, that will give you another constraint to use to evaluate the estimated CdAs.
The advantage of this method is that you can see when the run is spoiled and should be rejected. That is, you can spot a change in wind, or a passing car, or a change in other conditions. The sample size is the length of the run in seconds, not the number of total runs. You do want to have a wide variation in "entering" speeds so the runs are statistically independent and you can "pry apart" the estimates of CdA and Crr.
This method is a special case of the Virtual Elevation method where one uses an accurate power meter to collect the data. In this special case, we know that power while coasting is zero, so accuracy in power is not an issue. However, as in all estimates using Virtual Elevation, you will want your speed measurements to be as accurate as possible, so it's best to use a separate wheel sensor and to measure wheel roll-out accurately. Measurements of CdA attained using Virtual Elevation have been validated with wind tunnel measurements, and VE is the basis for most of the field tests done by pro cycling and Olympic teams. They use power meters not because the method requires it (the mathematics is exactly the same) but rather because data collection is faster: you can go both uphill and down, and it's easier to get a broad range of speeds since you can pedal. In typical coast downs, you are limited in the range of speeds you can easily attain and the length of uphill segments is short.
Once you have CdA and Crr, you can estimate the power "cost" in terms of watts from your flag at different wind speeds, not just at a given speed. The conversion formula for converting to power is given in one of the answers to that previous bike.SE question.