Here's one way you can do it.
First, upload the images to use for the mouseovers into your media library and copy the image links.
For each one, find the "title" attribute value and create a block of CSS like this:
a[title="Flickr"] img {
display: none;
}
a[title="Flickr"] {
display: block;
background: url(http://i1059.photobucket.com/albums/t434/frommartawithlove/BFlickr.png);
width: 210px;
height: 46px;
}
a[title="Flickr"]:hover {
display: block;
background: url(http://s.wordpress.org/about/images/logos/wordpress-logo-32-blue.png);
width: 210px;
height: 46px;
}
I used a WordPress logo as an example above, so you'll want to replace the value of the 2nd url() function with the Flickr image you uploaded to your media library.