I had family send stuff to me in Telic through the US military postal service. I went into the US post office and asked the postal address and also asked if it was ok to use the system. They were great and helped loads.
There's a couple of ways you can do this. My parents are in Australia so had a sinilar problem, they did it two ways. First one was my Mother going down to the consulate and getting someone in the MA's dept to post it back in the diplomatic bag. The other way was I was working at MND (SE) which had an AFPO (like a BFPO but Australian ) Mum sent the parcel to an Australian colleague who just passed it on. Just get whoever it is to take a walk over to the local Spam Postie with a pack of biccies/rank slide/cap badge and get their BFPO equivalent.
Mail from USA to a USA APO number in Iraq takes on average about 10 days if it is from a mail order type place. Strangely it takes a few days longer if it is privately posted (presumably due to delays getting to a main sorting office compared to the mail order firms having dedicated pick up/delivery direct to a main sorting office or some such).
If you share a camp with yanks and can get someone to loan you his/her address, that would be your fastest option otherwise you are adding US international post time to BFPO post time.
Whilst I was in Iraq I received post from family on holiday in Poland and Turkey, and loads of letters from my Mrs working in the US.
In all cases they just wrote the normal BFPO address on the envelope, and then wrote "GREAT BRITAIN" at the bottom. The foreign post office just dumps it into the bag for the UK when they see that, and when it gets to the UK it gets sorted as normal.
Postage cost was the same as it would be to/from the UK, from the UK to Iraq and vice versa was free as normal.
Letters from Washington DC took a week to 10 days most of the time, although some that were posted just before the postal strike didn't turn up for 6 weeks and were overtaken by other letters.