3/8 will work just fine, just be sure and use good quality transmission temperature oil rated hose and some very good stainless steel band clamps.
Last thing you want is a line blowing off and dumping all the ATF out of a transmission going down the road! 
I personally do not like screw clamps on any oil lines especially ones exposed to higher temperatures like transmission and power steering hoses as they can tend to work loose with age and can also damage the rubber hose when compressed and / or overtightened. Seen this many, many times over the years!
Instead, I prefer the OETIKER or Shark crimp type band clamps used on PEX and a few other applications. They are available at home builder supply stores, Gringer, plumbing supply stores, and Hardware stores. They work great on rubber hose, never loosen up, come in lots of different sizes, and do not damage the rubber hose when compressed as they apply very even pressure all the way around the hose! Discovered them years ago when screw clamps just would not hold the higher pressure air line fittings adequately on the ends of air line hose.
Some factory installed clamps are very similar in fit and function!
This is what they look like:
This is a picture of my Magnefine in-line transmission filter install on the Jeep CRD using crimp clamps and 3/8 transmission line hose:
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I'm sold! 