I want to free up storage on my new iPad Mini by transferring movies purchased on iTunes to a flash drive, and still be able to watch the transferred movies on my iPad with the SSD attached. Is there an SSD that will allow me to do this?

You can transfer and store purchased DRM protected iTunes movies to a flash memory drive or SSD, but iTunes movies must be moved back to the internal storage of the iPad in order to be played.

This is no workarounds are circumventing this fact.

Sorry.

Apple and The Motion Picture Corporation of America do not allow external streaming of any purchased iTunes movie or TV content from any external device drives, any longer.

Up until IOS 6, Apple left a backdoor process in the Safari Web browser to be able to remote stream purchased iTunes movie content through the Safari Web browser.

When iOS 7 was introduced/released, Apple permanently closed up that backdoor and ended any remote streaming of iTunes content from any external drive sources.

Sorry.

This is THE main reason I no longer, for many years now, purchase ANY more iTunes content from Apple's iTunes Stores and have gone back to purchasing physical disc media.

There are ways to do what you want to do using actual physical media and external drives with iOS devices, but none of that can be discussed here in Apple's “official” support communities as it is against the Terms of Use of these communities.

Internet searches are your friend for the answers you seek.

Best of Luck to You!