I used photobucket until they took my pictures hostage and added a watermark till I paid them money. I find their site very slow and hard to use although maybe it is handy with their app on your phone.

In photobucket on the right side of your picture there are several options for ways to link to the picture (I can't recall but it used to be one was HTML code, one was for posting a link in email, one was called 'direct' You have to fuss with those links as each is a bit different and put them in the forum software here using the full editor and the 'picture' icon. One of those settings did work to embed pictures into posts.