I found this information from MS to be insufficient, and pieced together the correct way to import data into SQL Server from a SQL file into an Amazon database using a non-standard port:
sqlcmd -S tcp:mydata.c960gorblahblah.us-west-2.rds.amazonaws.com,1337 -U username -P p@ssW@rd~ -d mydatabasename -i C:\DATA\MyDatabaseName.sql -o C:\DATA\results.txt
It displays here as multiple lines, but it's a single line. You should be able to copy-paste it anywhere by triple-clicking on it.
Note that I used "Tasks, Generate Scripts, Options, Advanced, Schema+Data" to generate the SQL file. Here's a page that shows this in detail. Follow the other links above if you need more detail on what's happening here.