Buy yourself an aquarium pump or something similar.
You could have it in a bucket, into which you're running your flat faucet, and still use an immersion chiller. The best part of this is that you can use the warm tap water to take down the temperature to something reasonable, and then start adding ice to the bucket so that your chiller can bring the wort down below the temperature of your tap water.
I can't hook my IC to the faucet for a similar reason, so this is what I do when I'm using my IC.