Aha, so there is no way of ssh-ing to an RDS instance directly (Chromebook or otherwise), as Fredrick mentioned.
That said, I have accomplished all I needed by ssh-ing from my Chromebook into my Google Compute Engine, and then hopping from there to my RDS instance, using the standard:
me@myserver$mysql -h myrdsinstanceaddress -P 3306 -u root -p
So, the crux is that you have to ssh into some other server, and then work from there.