union of Flying Instructors?
This is about as likely as seeing pink wriggly tailed flying objects.
You must realise that no union is viable unless a majority of the total group of whatever are members of that union.
Take a look at my last post. Even though in the UK, there no longer is an "self improvers" route to getting a CPL/ATPL, it is STILL possible to have plentiful of instructors just from the "doing it for fun" group.
In the UK, most small flying clubs will have a register of 30-40 such people that they can call on at any time - so there is a good chance that they can provide cover for any part of the week.