The thing I was thinking of above is called a “soundproof practise booth”. There are probably other terms for it as well. Just had a quick google and there seems to be plenty of links - including for a DIY approach…Lots of musicians and singers out there living in built-up areas, professionals and beginners with this problem - either real or imagined!
The cost of the soundproofing materials was always the sticking point. Maybe there are cheaper alternatives available now.
Garry
The maths get a bit scary if you think of making a sound resistant structure. If we look at the measurements I took of Grey Larsen (a not particularly loud player), we get levels up to around 85dBA SPL at 1 metre:
Conversational levels (which I guess is an OK level for an apartment) are around 50dB SPL, so we need an enclosure that loses 35dB over the flute range, say 250Hz to 3KHz. A single leaf of brickwork will achieve that, but the apartment owner might be a bit surprised to discover such a permanent structure in your lounge room. A sandwich of two sheets of 12mm (1/2") plasterboard on a 50mm (2") frame will also achieve that and could be disassembled.
The door to the structure is a bit harder - to achieve this level you need specially made acoustic doors, or an airlock with more typical doors at each end. Speaking of air, you’ll need a ducted forced air supply and return - the two 10’ lengths of ducting usually offering enough attenuation not to “short-circuit” what you’ve achieved in the walls. Not looking good, is it?
When I was learning flute and living in a hostel, I found an electrical switchboard cupboard beside the basement games room, and successfully sought permission to use that. I also used to wander down to the nearby lake and play on the shore (one day a fish swam up to me, so I thought that encouraging!). But that only works in the nice weather. The car is another option, but you might have to sit in the passenger’s seat and keep the engine running in winter!
Poster putty is looking better and better …
Terry
Hmm… Must be an English/Australian thing… Most right-hand fluters in the US find it easier sitting in the driver’s seat (left side)… 
My problem with playing in the car has been that the flute’s volume is deafening after a bit, bouncing back from the windshield. Which is lessened by opening the windows, but that sort-of defeats the purpose…
I still think local laws need to be a bit more specific, regarding fines, for something as (relatively) quiet as a lone flute in a closed apartment during daytime hours.
I’ve tried practicing, in the powder room/loo which is only about 3x5 feet. My advice is that if you’re going to practice in a place this small, you MUST wear earplugs. I do and my ears still ring if I play for a while.
Kirk
thanks everyone, very helpful. and thanks to terry for providing the data - confirms my suspicions. at least i have a good idea now on how to proceed, wherever i end up living.
Rama Lama Ding Dong, why don’t you just go on over and introduce your charming self to your neighbors? They will invite you in for a cup of tea. Then you can just ask them if they can hear you, and if they can, if it bothers them.
They will tell you either that they cannot hear you, and would you please play a bit louder, or yes, they can hear you, and would you please play a bit louder.
Roz says you should invite them to your place for a cup of tea. Then they will be in your debt.
Ignore what everybody else has said. It’s overkill.
well i’m in debt to yours and roz’s hospitality. that’s for sure. good food, good music, good company. and plenty of good flutes.