Did you mean MIL-H-5606?
I would second Maverick's question. If possible go with Nylaflow all the way. If you add a couple unions to change it to Tygon you are adding 4 more places for potential leaks. Using the KISS method is usually the best.
Tygon would probably work with the fluid, but it does quickly go from flexible to stiff. I am using it for the fuel return line from the header tank to the fuel tank and it has gotten very stiff.