djams,
First thing is to get in the pool and start practicing. Build up to it. Set your goal of either swimming X number of laps, then start increasing that, either that or set yourself a time limit to continuously swim. For the test you don't have to stick with a certain stroke, a lot of people either use breast or sidestroke. For myself, I can move pretty quickly through the water with a sidestroke.. anyways, once you build up to a mile, throw on a big t-shirt (long sleeves if you have one) and some baggy shorts or a pair of jeans. Then swim with those on. Of course tell the life guard what the heck you are doing, or they will go "what the hell!". That should more than adequately simulate the drag of swimming with a flightsuit. Do it in stages, and set yourself a goal. No reason to attempt it all on the first try if you aren't that strong of a swimmer.
Note, in API you go through the swimming classes, and they build up your endurance there. But I would caution weak swimmers to be more prepared, last thing you want to be is on the backside of the power curve when so much else is going on.
For those about to do that mile swim, vaseline works wonders on the chaffing points, under the arms, etc. when you have to swim. Couple people didn't put any on prior to it, and had big old red rashes from that 30-45 min swim.
Hope the info helps.