I've got a feeling that perhaps previously, flickr would offer an actual URL to the physical image (not a html page which it's nested-in),[ img ] code, and a few other useful little things. I suppose that's academic because regardless of whether they have in the past or not, it appears that it's not so straightforward now.
I guess you can only continue to find the URL to the image (the http:// part which ends in .jpg/.gif/.png/.whatever and not .html/.asp/.php/.whatever) and paste that into your post; or perhaps consider photobucket if you need to post a high number/frequency of images, as the last time I was logged-in there, [ img ] code / bb code were shown below each image in your galleries...
All the best,
Rob.