The brief answer is no, you possibly can't. I'm sad, but that is just the way it is.
However, all hope is not lost in spite of this terrible news. There are two major avenues you may go down.
The very first is to easily email the photos to yourself and then download them to the Kindle. This process works fine if you only need several holiday snaps or pictures of the little nephew's birthday or whatever, but its not much use for the great deal of pictures.
The second technique is a little more refined. With a hard drive, you are able to transfer photos relatively easily from one device to another, it will help you transfer a greater amount of pictures but will likely take a lot less time.
The best option, I think, is probably the second one, especially when you seek out the "eye-Fi" SD card, compatible with most recent cameras (though, as always, it's surely best to double check). Sime, of The Digital Photography School blog, was clearly impressed. In his review, he said,
"With the Eye-Fi X2 card, I could upload full res photos from my NEX 5 to my iPhone and then do what I wanted with them [Instagram / Facebook / Flickr etc] when you're using the X2 card, you can connect the camera directly to your iPhone / iPad without having to use a Wifi router etc You can also use the Eye-Fi app on your phone [iPhone and Android] to upload your images to your computer / Flickr etc. Yep - works, works well".
He then gave an individual account of the Eye-Fi's usefulness, that I've re-printed below.
"My wife and I went to the zoo with our almost-three year old a couple of weeks back and I had a look through her images afterwards, realising that there were images from her camera dating back to well, when I gave her the camera! She's currently using a 32GB SDHC card in there, and just leaves everything on the card! When I asked if she had copied any on to her computer, I was told "That's too hard / I don't have time / Where's the cable" (Yes, a combo of the three, I didn't press for details ;) So - I cunningly swapped out the existing card for the Eye-Fi card, loaded the app on her Macbook and added it to start when her computer starts, but to hide in the background (This is an option in the application) so basically, the camera connects to her laptop whenever it can and copies the photographs across - they are there, ready to use. Guess who won 'awesome technical husband of the week award?' (Obviously a lot of you are tech savvy, but well )"
By no means let it be said that I disregard an issue of yours devoid of producing a suggestion of my own.
You'll permit me a quick tangent, there is the line in one of those beloved books of my teen years 'Have Nice Day: A Tale of Blood & Sweatsocks' by Mick Foley (which is a immense book about life in general, even when you aren't a wrestling fan) that Mick says, "I'd always felt that it is not good enough to shoot something down - It is best to have a solution". Take that and work with it, people.
We found it here