The thesis was that Flickr, as part of Yahoo! and a large, established site, is suffering from an 'innovator's dilemma' — hamstrung by established processes, whereas Instagram can basically do as it pleases. There's a lot of name-calling and blame-assigning and it's not really worth reading unless you're into that sort of thing.
The larger question here, beyond 'is Instagram clobbering Flickr on mobile' (yes, almost certainly) is "can Flickr survive their slow start on mobile". The answer to that is a little more complicated.
Being Scrappy Pays Off
There's no denying Instagram is scrappier than Flickr. Instagram rolls out new features with stunning regularity, things like new filters and feed modifications. They also stay deliberately small — if you use Instagram you won't find sets or collections, you won't find organizational tools or really any sharing tools to speak of (beyond basic Twitter/Facebook integration). No permissions, minimal community, minimal data views, basic navigation. What you'll find is a sharply focused way to take interesting pictures with your phone, and share them with friends. That's it.
What that means is that when Instagram wants to iterate and stay a step ahead, they have a narrower problem to attack. Fewer concerns, more constraints — this all pays dividends in keeping Instagram scrappy in a way Flickr simply can't do.
Scrappy Isn't Everything
What some of the discussion thus far has ignored is that scrappiness and first-mover advantage aren't the whole game. Instagram didn't get to mobile photos first but they did get to interesting, trendy mobile photos first and that's paying off (for good reason - I use it too). Flickr, however, is building a photo-sharing ecosystem, with dependent applications and a host of complexity that Instagram hasn't touched.
Flickr won't pay the ultimate price for it's slow mobile strategy. Mobile is the future — adoption and expansion for mobile is off the charts, and will eclipse desktop use very, very soon, so Flickr needs to be scrappier; but that doesn't mean Instagram won the war (or was even a player in it, or that there was even a war). If Facebook has taught us anything it's that the 500lb gorilla in the room is that big for a reason, and no amount of scrappy upstart mindshare will topple it without a lot of work and considered problem solving (see: Twitter).
Instagram is great fun, and competition is good - but Flickr has time to adapt. Maybe this will be the kick in the pants Flickr needs to move faster, or maybe Instagram will continue to evolve. What's rad is that we win either way.