There are often different options as to how you can record anything. It depends on what the end result is going to be and how or if it is going to be mixed either solo or with other instruments. But I guess it is solo in this case would that be right.
If you don't have access to a nice space and you don't want the sound of a distant wooden flute in a room you can also record it reasonably close and capture all the fine detail and use a nice convolution reverb to add the ambience later. (And have a lot of control over that ambience) If you are going to do a closer recording I would not bother making a stereo recording either. It is a very mono point source sound and stereo wont gain much. Use the ambience you add to create the stereo imaging. (even if it's is quite low in the mix)
Both very valid techniques but sound different. Decide which one you are going for and then use the appropriate technique to get it.
I totally agree with
Daniel in that some instruments should not be recorded up close and violin for example is definitely one of them, but wooden flute is not though. That is one of those that can work well either way.