I just figured this out because I need to show the medium-size image. You’ll need to be a little comfortable with minor editing of 1 line in a Javascript file.
1. Use your FTP client to find the file “/wp-content/plugins/wordpress-media-flickr/wp-media-flickr.js”
2. Download the file to your hard drive and open it in a text editor.
3. Locate line #95, it should look like this:
'/'+photo.id+'_'+photo.secret+'_m.jpg';
4. Remove the “_m” from the line of code so that it looks like this:
'/'+photo.id+'_'+photo.secret+'.jpg';
5. Save the file and re-upload it to your server. Verify by adding a test image to a test post and previewing it in your site’s template. It should now be the size you want!
Removing the _m gives you the 500px wide image, so you can play with other suffixes to get the image size you’re looking for.