I believe the only way to do that would be to get the download into Amazon for digital download. Otherwise, people have to email it to their kindle accounts.

You can create a button from http://www.amazon.com/gp/sendtokindle/developers/button . If you like further qs about it you can send it to me so I will be happy to assist you.
By the way for ipad I advice you to send it to instapaper and evernote which is frequently used apps for reading.

Here are a few options to allow customers to send digital downloads to their iPad or Kindle from your WordPress site:

Use a plugin like Send to Kindle that will convert your PDFs to MOBI format and send them directly to a customer's Kindle via their registered email address.

Integrate with Amazon's Send to Kindle service by adding a "Send to Kindle" button next to downloads. When clicked, it will email the file to their Kindle email.

For iPad and iOS, you can generate an email with the PDF attached and pre-populated subject or message that they just need to send. Or use a plugin like Email Attachments to automate the email sending.

Upload PDFs to Dropbox or Google Drive and generate shareable links to the files. Provide an "Open in Dropbox/Drive" button to allow easy access from their mobile devices.

- Convert PDFs to ePUB format and allow customers to download the ePUB file, which can be opened natively in iBooks or third-party readers on iPad.

Look into services like SendOwl that will convert files, track sent or opened status, and allow mobile delivery across devices from your WordPress site.

The key is making it a one-click process for customers to get files onto their preferred reading devices without extra steps. Converting to optimized formats and integrating delivery services work best.