Hello, Amanda,
I did some research, and sadly I wasn't able to confirm that Rapunzel and Flynn Rider are making appearances to meet guests at Epcot. However, I do know that currently
Rapunzel meets guests at Princess Fairytale Hall at the Magic Kingdom. You can also see both Rapunzel and Flynn in the
Disney Festival of Fantasy parade. One thing to keep in mind is that characters do change, so make sure and grab a copy of the
Times Guide (located with park maps) to see if they are making appearances when you arrive at the parks. You can also stop by any of the park's Guest Relations and ask if they can check to see if they will be available during your trip.
I'll also let you in a fun
Tangled experience: searching for Pascal's friend near the
Tangled-inspired rest area that is located near the
"it's a small world" attraction in the Magic Kingdom. Hidden throughout the plants and nearby building, there are 10 chameleons to look for. And if you need some hints, a quick internet search can provide you with some!
Have a wonderful trip!
-Kara