Do I need to suppress ringing in a flyback converter?
Note that this answer was provided before the OP made an adjustment to the question.

Now my question is: Is it necessary to cancel it due to EMI emissions?

No, it's necessary to cancel the ringing to prevent an excessive back-emf damaging the MOSFET due to over-voltage. It's caused by leakage inductance in the primary and, any energy it stores during the charge cycle, cannot be passed to the secondary hence, it should be suppressed if too excessive. As a side-issue it can reduce some EMI emissions.