I can think of a couple of different methods to do the same thing.
1 - Standup your own photo web site, provide share links from there. There are several hosting providers out there, some very inexpensive. However, the maintenance responsibility. Several providers provide simple "one-click" installs of the software.
2 - I know photos.google.com also allow you to set up albums and share individual pictures. Have not tried to embed them into a forum yet, maybe I can give that a whirl.
With all that being said, I have had a smugmug account for years, since I use it for providing photo galleries to family. Works well and takes my maintenance responsibility out of it. Not sure what flicker acquisition will mean between the two.
Just my .02
Edit1 - just tried to link a photo from google and it will not allow me to use the extension on this forum. Going to try the next. One - here was the photo link: https://photos.app.goo.gl/sWly5OiOIzXLDi9s2
Edit2 - this was completed with smugmug and using bbcode - so that works, i guess similar to flickr - and yeah sorry, just fed them, so things are closed and particulate is floating. really need to get a gel for the cell phone..