[old_tv_nut]

Another way that just gets the image address without the added text and links:

On Flickr, click on the download arrow at the far right bottom.
A popup menu appears with several sizes and "View all sizes."
Click on "View all sizes".
This brings up a page with all available sizes listed.
Pick the size you want and click on it. When that image appears, right click on the image and select "copy image address" from the pop-up menu.

Back at your VK reply, click "Go Advanced"
Above the text box, click the "insert image" icon (looks like a postcard of a mountain).
In the popup for the URL, paste the image address that you copied from flickr by typing CTL-V, and click OK.

EDIT: incase you were in doubt, neither procedure actually copies the image to VK, only the link. Therefore, you must keep the image on Flickr or it will disappear here too.