I've been looking through the rules and I can't find anything specifically against it. When beginning RPs here, is there a rule against moving RPs that were started in other places (other sites, Discord, etc)?
No, you are free to write wherever you and your partner agree to write. Having said that, we do not permit poaching (to or from this site), so you can't solicit/advertise for elsewhere, "Come write with me at www.RPHERENOTATBMR.com."
We do not consider setting up an RP for email or discord as inappapropriate as long as it is exclusively for BMR members. You cannot bring in non-BMR members, as they need to adhere to our rules and we cannot protect our members from non-members in a venue outside of BMR itself.