Firstly, I googled "mute and flute" and came up with the following advice that may be of assistance to you:
(source: http://www.phys.unsw.edu.au/jw.....#flutemute )
Q Can you make a flute mute? Is there a way I can practise in the middle of the night without disturbing the whole house and at the same time learning how to play notes and music?
Two ways. Put a small piece of cotton wool in the headjoint. This works well on the low range, but less well at the high pitches where you will wake the neighbours. Alternatively, put a piece of modelling clay on the edge of the embouchure hole, just opposite where you blow.
Perhaps these are worth a try?
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My additional thoughts...
Can I also suggest that before you totally give up on the idea of playing indoors that you enlist a friend and/or neighbours to provide you with some objective advice as to exactly how loud you really are to the outside world when you play your flute in your apartment?
Shut the door, shut windows, close all the curtains and play your flute at various registers and using various dynamics (ie: low register, piano/ top register, piano/ low register, mezzo forte/top register, mezzo forte etc).
Your friend/neighbour could then listen outside your studio to see how loud your playing really is at various pitches and dynamics.
You should also experiment by moving to different spots within the enclosed space. It doesn't sound particularly romantic, but playing to a solid, external wall as far away as possible from a window (hence, no neighbours and no window for the sound to easily travel through) is likely to make the least amount of impact on your neighbours.
You may well find that you can play levels piano to mezzo forte without anyone outside your apartment even being aware that you are playing in the first place. Of course, it is more likely that low register of your flute will be easier on the ear, than the top notes. You may have to make adjustments for this when playing. At least you would know for absolute sure.
Other thoughts could be that you could consider joining a community type band or orchestra where playing your flute (sometimes as loud as you like!) would be incredibly welcome or as you suggested, playing in the park.
Finally, I just wanted to say that I'm so glad to see you embrace music, it truly does wonders for the soul!