How can I store least used table files to a slower drive?
What you are asking is not really an automatic feature in MySQL 5.6, I could be wrong.
Notwithstanding, you can set it up manually.
Given the following information

Your datadir is /var/lib/mysql
You data is in the Database mydb
You have this InnoDB table

Table Description
CREATE TABLE mytable
(
   if int not null autop_increment,
   ...
   primary key (id)
) ENGINE=InnoDB;


You have a data folder to hold the least often used tables called /data/least
Make sure /data/least is owned by mysql  by running chown -R mysql:mysql /data/least

Here is what you must do manually
USE mydb
CREATE TABLE mytable_least
(
   if int not null autop_increment,
   ...
   primary key (id)
) ENGINE=InnoDB DATA DIRECTORY='/data/least';
INSERT INTO mytable_least SELECT * FROM mytable;
ALTER TABLE mytable RENAME mytable_trash;
ALTER TABLE mytable_least RENAME mytable;

How was mydb.mytable manifested before the change ?

The .frm file is /var/lib/mysql/mydb/mytable.frm
The .ibd file is /var/lib/mysql/mydb/mytable.ibd

How is mydb.mytable now manifested ?

The .frm file is /var/lib/mysql/mydb/mytable.frm
The .ibd file is /data/least/mytable.ibd

You should test this out with a blank InnoDB table and make sure.
Give it a Try !!!