Of course this can be done manually, but for the sake of keeping things organized and simplying adding things in you can use a WordPress plugin called Photonic. It integrates into the Upload/Insert dialog and allows you create in post galleries from Flickr, Picasa, SmugMug, and 500px.
Adding Flickr first requires adding the Flickr API key. There is a link directly in the Flickr section of the plugin settings. Then you have to get your user ID from your photo stream URL. There is a link to a site that will tell you it right in the plugin’s upload dialog. The string is fairly easy to recognize, as you will see a string of characters like 83678835@N00 at the end of the URL when you go to your photostream.
You can then customize your selection by narrowing it down to certain tags, or a specific gallery. Below you will see my complete photostream.