Haha, yeah, but then, that's Amano's art for you.

(Interesting tidbit, is that 'pink featherless flamingo' design ended up being used in the FFV sequel anime
Legend of the Crystals, so take from that what you will.

).
And yes, is is definetely possible to ride ostriches
and emus, they're strong enough to bear a light rider... the main issue is their lack of easy domestication which is usually the requirement for a mount animal.
As for the gastornis and the chocobo's design, may I now also present to you
Bullockornis, aka the 'demon duck of doom' which is an example of extinct Australian megafauna, of which modern artists' imrpessions seem to scarily depict something
very similar to the chocobo... but that's just coincidence (and proof that Australia really is a FF world in reality... but I digress

).