I have a Snap Circuits kit which has this oscillator circuit which I am fascinated with. I know how a relay buzzer oscillator works and it is pretty cool. This circuit uses a potentiometer, polarized capacitors, and bipolar transistors. I am familiar with these components. I am just trying to figure out how this circuit works and why the light flashes/the speaker pulses when I turn the circuit on and where the circuit flows. Can someone please help me figure this circuit out? Thank you very much.
Yup, this is an interesting little circuit. Pulse circuits can be a little tricky to try to figure out at first, but don't get discouraged. It's a good idea to draw a diagram of the circuit and write the voltages you think will be at each location on the circuit. You could also but some arrows for current flow and write how much current would flow through that point on the circuit.
If you start with all capacitors discharged (let's call this T0, when the switch closes), you can think of them as a short circuit for the very first instant that the circuit turns on. After a microsecond or so (let's call this T1), they start to charge and some voltage builds across their leads. This changes the balance of voltages and currents in the circuit and you can make some calculations about how fast the capacitors will charge and write the new numbers around the circuit for voltages and currents.
Then look at the active components (transistors & ICs) and the voltages applied to them. As you work your way around the circuit at different times, you'll start to see how the circuit works.
I threw together this schematic so you can see how it would look to transfer a snap circuit into a real schematic diagram. I included a resistor that the Snap Circuits folks hide from you inside the plastic cover so you don't get any crazy ideas about how diodes work.
I highly recommend the book Getting Started in Electronics by Forrest Mims, III for people just getting into electronics. I used it back in the 80s when I was learning on my first 300 in 1 electronics kit (the old school version of Snap Circuits). If you're already past that level, jump to something a bit more complicated like The Art of Electronics by Horowitz and Hill.
Have fun learning electronics.
Additional Edit: As an aside, replace the 10 uF C3 with the 0.02 uF C1. This gives you a rudimentary PWM brightness controller. C1 is not polarized so you can flip it either way in the circuit.