Simple Fire Alarm Circuit using transistor not simulating correctly
There are a couple problems with the circuits used from that site. One, they are using an NPN transistor incorrectly and two, a speaker can't produce sound when you apply a constant voltage to it. The only circuit that would work is the one using the lm358. 

Now onto your circuit. Couple problems with it: 1) Incorrect biasing of a PNP transistor or rather incorrect orientation. Also note you're using what seems to be a symbol of phototransistor (?). 2) Battery is in wrong orientation. 3) Speaker won't produce sound just because you apply voltage to it. 4) Don't see why you need a capacitor here. 

Here is a more practical circuit which should work: 

It uses a NTC thermistor which at 25 Celsius is about 10k but at about 70 Celsius is 1.7k. When the temperature is room temperature or at least way lower than flame, the NPN transistor is off and buzzer is off. When flame is present and within a few inches of Thermistor, its resistance drops to about 1.7k and biases the transistor on thus activating the buzzer. Note that flame should be a few inches away to achieve 70 degrees Celsius and not directly applied to thermistor. You can test this out when prototyping. Also circuit uses NPN transistor biases correctly and a piezoelectric buzzer not speaker. Circuit can be power off 3xAA batteries. 







simulate this circuit &ndash; Schematic created using CircuitLab

Edit: To show how With some modifications to your circuit it should work:

Your new circuit:







simulate this circuit