Did some digging (if you could even call it that, because I found this embarassingly quickly), and, as others had reported, there were multiple possible flag animations for the like button. Which flag would show up depended on the tags used in the liked post!
The Philadelphia Pride flag was probably used when liking posts with the #pride month tag, and while that's a great step up from just the rainbow from the Gay Pride flag, the decision to not include the Trans and Intersex Pride flags' colors stands out in juxtaposition with the increasing visibility of just these demographics in recent years.
I'm willing to bet Tumblr staff saw this post, and ditched the idea of tag-dependent animations in response, having the Progress flag colors play for all posts with queer tags. What I don't know if there was a priority for which flag would play for posts that have multiple queer tags, or if one valid flag was chosen at random.
Huge thanks to @sufferingfrommoodpoisoning for including GIFs of the removed animations in this linked post!
(Found by looking up "like button" in the earch bar. As I said, embarassingly easy...)
With that out of the way,
my goal with these additions was to find answers, present them, and to, ultimately, direct people's attention back towards the point of the original post. This whole thing is the symptom of a greater ongoing problem within Tumblr.
The blogs of trans users are still being mass-reported and auto-deleted, with @staff still not willing to do much of anything to improve matters, as we've seen. If anything regarding the site, let's keep that in mind and act accordingly moving forward!
(That, and what kind of person Tumblr's CEO, Matt Mullenweg, is.)