I’ve downloaded the FSM from https://playground.arduino.cc/Code/FiniteStateMachine; is that the version that you’re using? If not, please post a link.
Your code will compile in newer IDEs (the system I’m working on has 1.6.6 installed, did not update yet) if you include Arduino.h instead of WProgram.h in FiniteStateMachine.h
By the looks of it, there are newer versions of the library that might have solved the above problem for you.
and if you add the function prototypes in the beginning of StandaloneBurner.ino
// function prototypes
State Off = State(enterOff, updateOff, exitOff); // burner is off
Not sure what you mean by “earth trigger”. Pins 2 and 3 (from your diagram) control the respective relays. Both of those relays miss one wire in your drawing (by the looks of it); a relay has two (or three) pins that you connect the ‘device’ to (in your case the valve or the igniter) and two pins that are connected to the Arduino.
I will see what I can find about the flashing led; not familiar with the library so might not be able to find it.