Simply dump the production database using mysqldump and the following options:
mysqldump --single-transaction --master-data=2 -C -q
If you are using InnoDB tables, this will dump your database to a file without locking the tables (--single-transaction) AND save the bin log position in that file as a comment (--master-data=2). This is important because the dump itself takes a while to complete and loading it into RDS using the command below takes another 30 minutes to an hour in our case, and we didn't want the site down for that long as I mentioned before.
mysql -u root -p -h
mysqlbinlog mysql-bin.002971 --start-position=73319797 | mysql -u root -p -h
Then, when everything was ready.. all I had to do was put up our maintenance page, sever all connections to our production database, run mysqlbinlog one last time to make sure RDS is fully caught up (which only takes a second since we made sure it was very close already), switch the IPs, and re-deploy our app. After that, the maintenance page is removed and all traffic starts flowing to RDS. Thinking back, it was a pretty simple procedure, but it definitely took us a while to figure out what to do... hopefuilly this will be useful to anyone else thinking about moving to RDS.