Short answer: No.
1) The Kindle has two components: the Kindle as device and Kindle as eBook file format.
2) People have made an investment in Kindle books. Those who decide to switch from a Kindle device will use the Kindle app on the iPad. This really doesn’t wipe out the Kindle as such. It makes it a parasite inside the iPad. And those Kindle users will continue to buy Kindle books because what reason is there to split their library into Kindle and ePub (ePub equalling iBooks, Nook, or Kobo)? As I discovered for myself, Amazon offers more books that anyone else and it’s likely to stay that way. Amazon will also push books more than Apple will.
3) There is still a place for eInk until something comes along to make LCD/LEDs in bright sunlight possible. Pixel Qi’s status is still questionable. No one other than Notion Ink (which is still vaporware) has publicly stated it will use that screen — and even then, they curiously offer a model with a conventional LCD screen. Plus, Apple loves its IPS LED screen because it makes colors pop.
4) A smaller iPad would still weigh more than a Kindle. An iPad would most likely be the same size and weight as the Pandigital Novel, which also has a seven-inch screen:
Pandigital Novel: 7.5” x 5.5” x 0.5” – 16 oz
Barnes & Noble Nook: 7.7” x 4.9” x 0.5” – 12.1 oz
Amazon Kindle 3: 7.5” x 4.8” x 0.335” – 8.5-8.7oz
Sony Reader Touch: 6.9” x 4.8” x 0.4” – 10.1 oz
Kobo Reader: 7.24” x 4.72” x 0.393” – 7.795 oz
5) A smaller iPad will still cost more than a Kindle. This makes toting it around more of a financial risk.
6) A smaller iPad will be the New New Thing to steal. Theft anxiety is not conducive to relaxed reading in some public places.
7) A smaller iPad is likely to impact iPod Touch sales more than Kindle sales.
8) Amazon can always put the squeeze on its suppliers and further crush the price down from $139 for the WiFi version.
All that being said, everyday people are very fickle. They once paid $399 for a Kindle. If a seven-inch iPad came in at $299, people could make do with the limitations of an LED screen in bright sunlight (by sitting in the shade) and all the rest of the reasons I set out above. Especially that bit about theft risk — a $399 Kindle was a lot of money to wave around!
Plus, even if it didn’t wind up killing the Kindle device, it’d still outsell it at least twenty-to-one.