In the row of icons on the reply page that starts with the bold, italics, underline etc there’s an icon about 3/4 the way along labelled “image link” if you hover your mouse over it. It still needs to be a link somewhere, not to an image on your own PC, so you may still need to use Flickr.
Click that and a box will appear that you can paste the image link into. Click “insert” and it should appear when you submit.