Sadly not; you can't download most ebooks to your Kindle or other ereader. You can however download them to your:
- mobile phone
- tablet
- laptop
- desktop
To do so, you need a special app called Adobe Digital Editions.
Exceptions
A small number of DRM-free ebooks can be downloaded as regular pdf files. Also, chapters or pages of ebooks can be saved as regular pdf files and can be transferred to, and can be read on, eReader devices such as the Nook or Kindle.
Further reading
Library tutorial on downloading and installing Adobe Digital Editions
Adobe Acrobat: How to Convert a PDF to Kindle