How to create a local backup of a remote Amazon RDS MySQL database?

How do I create a local backup of a remote Amazon RDS MySQL database? What I need to know is how to make a complete full local backup of a MySQL database (not a remote Amazon snapshot) that can be used to restore to a new database anywhere, on any MySQL server (same version of course).

NOTE: I know how to import data from a flat file via MySQL. Here is how I connect:

mysql -h mydb.xxxxx.us-east-1.rds.amazonaws.com -u myuser -P 3306 -p

Here is how I load a single database table:

mysql> LOAD DATA LOCAL INFILE 'C:/Temp/t1.tab' INTO TABLE t1 LINES TERMINATED BY '\r\n';