I second the custom cell phone case idea. Although I think it would have to be a very well-designed cover that incorporates your name/logo in a non-flashy way so users don't feel like a walking advertisement.
The kite idea suggested above is fun, but perhaps too youthful for your target demographic. If you aren't dissuaded by that, I would suggest executing the same idea, but replacing kites (which are hard to fly) with balloons--if possible, in the shape of a chat-bubble--in green, blue, and gray (iphone text colors). Balloons are more tied to your app's concept than kites because they look like text bubbles. You could pass out a few hundred helium balloons on strings in a crowded public place. Photographed from above, it would look like a bunch of people walking around with iphone chat bubbles above their heads, which could be a very cool and meaningful image for your social media campaigns. Bonus points if you can figure out a non-gimmicky way to make the connection between physically popping the balloon and your app's purpose (eg, erasing the text or otherwise preserving the privacy).