I am trying to understand SR flip-flops from a book which uses the above circuit to describe different states that this circuit can get in. Initially, both the switches are open and the current flows from the output of left NOR gate( highlighted in red in the image). However, I am struggling to understand as to why both the inputs to the left NOR gate are zero and the right NOR gate aren't since their inputs are dependent on each other's output. In other words, why can't we assume that since in the beginning we have no input voltages to right NOR gate the output should be 1 which will mean that the current will be between the wire connecting output of the right NOR and the input of the left NOR?
When an SR latch like this "wakes up" as power is first applied, it will (in practice) be in either the state where the output is high or the output is low. We can't look at a circuit like this and know what its initial state will be. My hope is that the book says somewhere "suppose that the output is initially..."
I have a big problem with this example because when the switches are open the input voltage for the NOR gates will be unknown. A proper schematic would have an explicit pulldown resistor from each input to ground.
I think you also have a misunderstanding about the flow of current. In general, no current (actually, negligible current) flows into the input pin of a gate. So, the left gate never supplies the current that makes the bulb light up. This current always comes from the right NOR gate. How is this possible? Each gate has implied connections to a power supply and ground, so when the bulb is lit the current is coming from the power supply through the right hand NOR gate.