I tried using the iphone flickr app and you are right, it does not let you choose what kind of link, it does not offer the BBCode option.

On a desktop, when I open the link and use the bent arrow "share" button in the bottom right, there are 4 tabs across the top, "Share","Embed","Email", and "BBCode". The first tab gives the link you used. The last tab "BBCode" gives the one I used which is a clickable picture. Clicking on the picture opens the same web page as your link.

{url=https://flic.kr/p/2fsGYf4}{img}https://live.staticflickr.com/7818/47559909871_51a6a5e63e_m.jpg{/img}{/url}
Using curly brackets instead of square so you can see the code, the url part of the link is the same as your link. The stuff after img refers to an actual picture file on the flickr servers that ends in .jpg so that it works as an image link, but I don't know of any way to get that using a phone.

This is what it converts to
[Linked Image from live.staticflickr.com]