Updated info iTouch, iOS4
I have an iPod touch with iOS4 (jailbroken) installed and what I found varies a bit from what has been already discussed. When I use iPhone Explorer I see 2 hives, Apps and Root Directory.
I didn't see Kindle under Apps so I started digging around. Under Root Directory>User>Applications you will find a bunch of directories that are named with some type of GUID. If you expand Applications on the left panel and click the first one you will see the sub folders one of which will be named in a way that it can be matched to an app. If you just hit the down arrow you can cycle through them pretty quickly until you come to one that has Kindle.app in it.
In this same directory you will see the Documents folder. You can copy your .mobi files straight into this folder. If you have cover art all you need to do is rename the image file to match the name of the .mobi file you copied without the extension and copy it to the LibraryCov folder.
To get this book to show up in the Kindle app on my iPod I had to do a complete power off (hold the top button for 5 sec and you will see slide to power off.) Turn it back on and you should see the new ebook in the Kindle app.