First, let me commend you on your playing. It sounds very good to these admittedly "amateur" ears.
Listening to the recording on the video, the first thing is that you have a fairly lively room. It makes the reverb very short, and gives a somewhat hollow character to the sound. The piano and flute both show the same "space". I don't know if changing rooms is an option, but it would help to have some type of acoustic treatment to tame the reflections.
In addition, having the mic 2-3 feet away will not take advantage of any proximity effect that you typically get with a cardiod microphone.
To add lows to your your recording, try moving the mic closer to your flute, like 8-12 inches. You should get more direct sound, and perhaps a more even response. Also try adjusting the position between mouthpiece and keys. The downside is that if you are using the same mic to record the piano, its going to change that instrument's sound.
As for reverb, you can add very realistic reverb post recording. You won't get the type of long reverb that comes from a concert hall when in a typical living room.
Experiment as much as possible. Unfortunately, if you want a balanced recording of both the flute and piano in that room you may be looking at multiple mics to optimize both instruments.