Overall, using the Kindle app for the iPhone has been a positive experience. Here's what I like about it:
I always have my phone
So I always have any books I've loaded into the app. That's not true of the other books I'm reading, and probably wouldn't be true of a full Kindle (were I to buy one (which I won't)).
Reading is surprisingly easy
I though it would be more difficult, but it is very natural and almost as immersive as reading from a physical book... and actually more immersive than reading some awkwardly sized or poorly put together books.
The backlight is also nice, when trying to read in the dark without waking either my wife or my 1-month-old baby.
It's quick, easy, and relatively cheap to get books
I wish the interface were a little clearer, but in general it's got the same ease of use as the iTunes store... making it really easy to spend your money on their product!
It's not all great. And unless they can accommodate all the free books on the internet (as far as I know they can't), they will ultimately lose the market to somebody who can.