I have managed to work out the answer following the info found here:
https://meta.discourse.org/t/nextcloud-images-not-displaying-in-discourse/148908/2
Say you wish to display an observation photo for instance:
First find the image on iNat that you want, and get the URL that points to it. E.g. if on a desktop web browser, right-click on the image and select the option that (depending on what web browser you are using) says something like Copy Image Address, or Copy Image Link.
Then, in the forum reply, type ![] followed by the copied URL pasted in parenthesis (). You should end up with something like the following:
You can alternatively use the longer prefix ![image] . Both approaches appear to give identical results.
Finally note that depending on where you copied the link from, the link will end with any of small.jpeg, medium.jpeg, large.jpeg, or original.jpeg to indicate which image size variant you happened to be looking at. You can freely change this in the URL to whichever size is desired with reference to the preview that should display to the right of your post draft.
E.g. here is the result of using the above code as shown with the small.jpeg image size:
I hope all of that is clear 
EDIT: For changing the displayed size of the image, no matter the source, see:
https://meta.discourse.org/t/default-image-size-in-posts/235465
https://meta.discourse.org/t/changing-image-width-height-manually-does-not-always-work/86649
There are two different approaches we can use as tested here using one of my photos shared via Nextcloud:
<img src="upload://zO2rftRX9gli92kh3UahRl66fK0.jpeg" width="200">