Best way to setup a process for emailing a dynamic security group in Office 365

Dynamic security groups are not mail enabled, so you cannot use them for that purpose. You can create an Office 365 Group with dynamic membership from the same place though, and that will do the trick.

And to correct your latter statement - you can add other security groups as a member of mail-enabled security group, however as those are not recognized as valid Exchange recipients, you will still not be able to use them for email purposes.