The fittings pictured are Parker fittings 37* flare nut, not inverted nut, 45*(auto style)
A person should use 37* flaring equipment when using 37* fittings.
That said, I have been using my 45* double flare kit for 40+ years and have not had leaks.
(Boy, I'm gonna catch flack saying that, but it is true.)
I agree that lines should have some kind of bend to eliminate vibration.
The double flare, and the sleeve on parker fittings, prevents cracking of the line @ the fitting.
Vibration harmonics will destroy a line if they are allowed to occur.
So bends help upset this harmonic vibration.
Longer runs are more prone than short.
Many times a simple tubing clamp or two will be suffice.