I've tried to mess with the available presets for export, but nothing seems to quite get at the issue. Original Illustration created in Illustrator and then imported to Animate. SWF file looks great, but had to make a H.264 for Instagram... but the colors are super muted (okay maybe not super, but still off-brand for this client) I'm doing more animations for them and would love to figure this out. Here are two side by sides from two different animations. Original correct on the left screen grabs from the output video file on the right. In looking there seems to be some fixes for Premire Pro with similar issues, but they don't seem to apply here.
You can export a png sequence and then render the video in Premiere if those fixes you mention work there.
I've always noticed that h.264 has issues with bright reds and oranges softening the hard edges of solid red and orange shapes. But it is similar with JPG as well... These codecs are not optimised for flat-colored animation, but for live video.
Nick - Character Designer and Animator, Flash user since 1998 Member of the Flanimate Powertools Team - extensions for character animation