Little mechanical tweaks may help (or sometimes just a fresh tune-up), but the bottom line is that you're up against physics. It takes a certain amount of energy to make an object of a certain size, shape and mass move through the air at a certain speed. Air resistance is the biggest energy consumer at highway speeds and increases in proportion to the square of speed, so the tweak that makes the most difference is reducing speed.
Interesting thing is that two different vehicles that get very different gas mileage when not towing often get about the same under tow (assuming the same trailer and towing conditions). The smaller, more economical vehicle simply has to work harder.
My Pilot gets 23-26 mpg (US) on the highway when not towing, and 17-19 towing our 13' Scamp
. It can drop down to 10-12 against a headwind. We got 27 recently on a trip to Monument Valley with a strong tailwind. We tow at around 60 mph in level, windless conditions on rural interstates. Your Flex is similar in size, shape, and engine displacement. Your trailer is a bit longer and boxier. How does your experience compare?
This thread has some data you may find useful for comparison: Tow Vehicle & Trailer combos - POST INFO