I just tried it on an iPad2 running iOS7 in Safari. It still works. Select image, select share arrow, for adding link to web pages select embed tab. HTML code will be in the middle of the window. For discussion forums like RFF select the BBCode tab. Again, the code will be in the middle of the window.
The only change has been they throw in extra code for attribution back to Flickr. Just delete the code you don't want.
~Joe