If you have downloaded a Kindle eBook from a 3rd party then you have a .mobi file on your computer. To read this on your iPad iTunes has a built-in function through which you can transfer these files to your iPad like you would music or a video file.
Step 1: Connect your iPad to iTunes and let it finish doing its inital backup/sync etc.
Step 2: Click on iPad tab in the upper right hand corner (in my case, Luke's iPad)
Step 3: Click on the Apps Tab in the top row, and scroll down to File Sharing Section
Step 4: Click on the Kindle App and then choose Add.. in the lower right corner.
Step 5: Now browse your computer to select the files that you have downloaded from your 3rd party (.mobi). When you select them they should appear in the window like below.
Step 6: Click Sync in the lower right corner.
Viola, your Books will now appear under the Devices Tab on your Kindle iPad App.