The button is not supposed to be used for ignition but to manually momentarily bridge the sensor to get the solenoid valve to open the fuel supply to the burner.
I presume this is for gas.
Something like on all new gas cookers.
To light the burner you have to press the knob to get the valve to open and allow the flame to ignite. Once the thermocouple detects the flame, the valve holds.
When the flame goes out, the valve closes via the thermocouple to prevent the gas escaping.
This is what I meant.
Assuming that this flame sensor outputs a high state when it detects the presence of a flame, the relay in the module with the relay will switch on and apply voltage to the solenoid valve.
When the flame disappears, the relay switches off and interrupts the power supply to the solenoid valve, thus interrupting the fuel supply.
In the initial state, there is no flame and the sensor will not allow the solenoid valve to switch on.
And this is where the button is needed.
The connection of the modules is simple.
You connect the + connector of the sensor module to the VCC connector of the relay module and connect it to the plus of the 5V power supply.
You connect the G connector of the sensor module to the GND connector of the module with relay and connect to the GND of this power supply.
Unfortunately, you need a 5V power supply here because the modules are supplied with 5V.
You connect the DO connector of the sensor module with the IN connector of the relay module.
The relay contacts, which are normally open, are connected to the solenoid valve circuit.