It's a fact that Instagram is the most popular and largest image sharing system. I'd guess that the amount of images on Instagram by itself is already several times larger than the rest of the internet combined. If Kagi wants to offer the best image search, it is essential that Instagram is included as a source.
Does Instagram (Meta) offer any APIs that Kagi could integrate with, and if so, with what kind of pricing? The search function within Instagram is of bottom-level low quality, which means that Kagi could offer something different. For people not loving Instagram, they could easily block those results from Kagi, for example if Instagram demands you to be logged in to see an image.
When doing a comparative search on Google Image Search, they do have access to Instagram and will surface a ton of Instagram images when you add "instagram" to your query. They also have access to images on Facebook, probably within the same deal.
With some effort I can get Kagi to surface some image results from Instagram, so there is some kind of indexing I assume, but for example let's say I search "stork bird instagram", on Google I get endless results from Instagram, on Kagi I get zero. So something is missing in the algorithm .