When you click on the share icon on Flickr choose bbcode.
Paste the code you get into your reply window. An example from mine gives this:
[url=https://flic.kr/p/953qr2][img]https://farm6.staticflickr.com/5002/5296592539_957e8a6f8f_b.jpg[/img][/url][url=https://flic.kr/p/953qr2]Aquilegia[/url] by [url=https://www.flickr.com/photos/acorn_sky/]Acorn Sky[/url], on Flickr
This will work, but if you put a return in after the [/url] in the middle it will look better. Like this:
[url=https://flic.kr/p/953qr2][img]https://farm6.staticflickr.com/5002/5296592539_957e8a6f8f_b.jpg[/img][/url]
[url=https://flic.kr/p/953qr2]Aquilegia[/url] by [url=https://www.flickr.com/photos/acorn_sky/]Acorn Sky[/url], on Flickr
That should give this:
Aquilegia by
Acorn Sky, on Flickr
If you don't want the text underneath the photo just use the bit of code that has the img tags around it. From mine that would be
[img]https://farm6.staticflickr.com/5002/5296592539_957e8a6f8f_b.jpg[/img]
which gives