I don't think Flickr and Facebook/Instragram really compete, except in the situation where people didn't need Flickr but Facebook/Instagram didn't exist yet. Flickr is more for professional photographers, not a social network for youths to share their photos with their group. If Flickr loses professional photogs, then they're hurting. But they haven't yet.

Instagram is not going to replace Flickr for Flickr's core audience.

I think flickr gradually became a place "more for professional photographers" as the rest of its uses were eroded by other social media sites.

Thats the entire point. Flickr is about photos. If Flickr was releasing new products and testing new things they might have landed on Flickstagram. But like OP said they didn't do much at all, and so missed the boat.

So yes you're right, they don't compete. But thats the problem. Hypothetical one, and I wouldn't blame the CEO for it. Its just one of the many things up the road they didn't travel up.