dtmstr
Emanualtop is probably right that you need a simulator to get a good representation of the flare.
But you stated that you are pretty close right now, just having problems on cold and windy days.
I am going to assume that you have an enclosed flare?
If so then you probably have a forced convection fan and some natural draft dampers
The stack should be insulated on the inside with rockwool insulation, that should keep your radiation down to a minimal amount.
This also keeps the stack metal temperature below 400F so the paint does not burn off.
So to figure out how much additional heat you need you need to do a rough heat balance around the stack. Use the current stack control temperature as the desired temperature. From the fan curve and motor amps you can get a rough estimate of the forced air coming in. You said you know the gas volume coming in and the heating value of the gas. The only thing left is the natural convection of cold air in the bottom. You can get that from an anemometer on the damper when it is running. So then Heat Out = (Forced air + natural convection air)at Control temperature. Which is equal to Heat of combustion of your biogas.
To get your propane requirement, increase your outlet temperature to the new desired temperature and the additional heat that is required will be the propane requirement.
The propane heat should only be about 25% or your current heat load.
Then I would calculate out the size of control valve I need for the propane assuming the valve is only 40% open.
That should give you some lead way in case you undersized the valve.
So your risk is really only that you could need to resize the valve if it is not working correctly when you get it all installed.
That is what I would do. It is rough but remember you don't need the exact value, you need to be close enough for the control system to function and that is all. Under heating is pretty easy to correct. Overheating is a bigger problem.
You also might want to consider installing an L shaped fence about 15ft away from the flare stack dampers to block the wind from blowing into the stack. This can be a problem in very windy locations.
Regards
StoneCold