All flexible designs I've seen are printed in a way which force you to either have a huge amount of color changes, and waste. Or go with a single color for the entire object. I've designed this egg to be printed in parts and snap together as well as printing them sequentially on the same plate. This way the amount of color changes is reduced from more than 300 to 3.

The parts are laid out for a sequential print profile contributing to the saved waste. If you change colors keep them matching the same way or reorder your objects and double check that they are printed for the least changes. If you want to make multiple eggs you could of course place all same-colored piece on one plate each. If you separate color by plate make sure to switch back to printing by layer.

Snapping them together might require some strength as it's designed to not fall apart easily once put together.

For those only interested in a single-color flexible egg I've also included a non-snap print-in-place version.