First, I have to say that I do have children, so my answer is pure speculation and imagination about what I would do if I had kids.
I think that I would encourage my children (if had any) to read from books initially unless I could find an e-reader that was in my price range that had colour as small children enjoy picture books and bright colours.
Once they started to see the pictures in their own heads, I would encourage them to read from both a kind and a book. Books can be borrowed from the local library (cheaper for parents) but children these days are very tech savvy so I guess it would not be long before they were reading on a kindle, iPad or a mobile device.
Oh how things have changed since I was a little kid!
I think it would depend on the age of the child. Kindles have their advantages, they're compact and easy to handle, the font size can be adjusted etc., but for young children there will always be something special about opening a book for the first time and enjoying colourful glossy illustrations, lifting the flap to discover who's hiding beneath or having a picture 'pop-up' when they turn a page. One of my childrens' favourite books had little pockets on each page with hidden surprises - not quite the same with a kindle.