I'm afraid that you might run into trouble with copyright/ebook licenses issues if you just decide to give away your favorite ebooks on your blog. That's the prime reason majority of ebooks are DRM'd so people can't just give away the ebooks they've bought.
The only time I know it's okay to post free ebooks is if the publisher/author is doing the giving away themselves. Or if you have the permission from an author to give away free downloads of his books. (i.e they have free coupon offers or giving the book as a gift via Amazon/Kobo)
You don't own an eBook when you buy it, it's like software so you cannot giveaway your Windows operating system (for example).
I, however, do giveaway eBooks on my blog as part of a promotion coordinated with the publisher / author.
I don't think I made myself clear in my first reply to this query.
I meant, if she had her book on Kindle (as an author of the work) then I thought she could send out a few free copies from the Amazon site. I didn't wish to imply that she could purchase it then send it out to anybody.
Hope that's clearer now.
amazon/Kindle have just introduced a feature which allows users to 'lend' a copy of certain titles to another person. Handy if you just want to show a friend one of your favourite reads.
Publishers often supply print books for giveaways so maybe they would do the same for an ebook? Or you could possibly contact the author and tell her/him you loved their book so much you would like to do a giveaway on your blog and see if they would be willing to send an ecopy to the winner? You could even invite them to your blog for an interview or guest post to go with the giveaway. I'm not sure which book you want to do this with, but if it is a hugely popular author you may not get a response. If it is a B-list or indie author you may get some interest. If it is an indie author I would say almost for sure they would say yes.
Also, if you are willing to pay for a copy yourself, you can use the new Kindle ebook gifting feature to send the winner a Kindle version of the ebook. I think Kobo may also have a gifting feature, not sure.