If you inspect the code you copy from Flickr you will see the image tags as part of what you are copying. The other parts of the code Flickr gives you create a link (the url part) back to Flickr and a title and some stuff that says it came from you on flickr.
when I wrote my reply above I was referencing a method to make any image url (something starting with http: and ending with .jpg) appear in line in your post. I described this method because KulaCube had the url handy.
The method you use to post from Flickr is preferable in many ways.
in my bag: e-m1, 7-14mm pro, 14-54mm mk ii, 50-200mm mk i, 70-300mm
in my pocket: e-pm2 lumix 12-32