Powering on specific pieces of circuitry in sequence
Your logic is, in principle headed roughly in the right direction, but there are a few problems. In the first place the 2-input OR gate is redundant, since the right-most FF ouput will force the NOR output low. More importantly, you show no means to reset the outputs to the correct starting state.

Generally the useful approach (using discrete logic) is to use a binary counter and a demultiplexer. The nominal part number for a demultiplexer is 74HC138/238, which will take in 3 address lines and some enable lines, and produce a 1-of-8 output. You can use 2 of these to decode 16 lines, and expand to virtually any number of outputs. The difference between the two types is that the 138 produces 1 low and 7 high, while the 238 produces 1 high and 7 low.

You also need to provide a reset to the counter to ensure that it starts at a count of zero. You might think that a counter would always do this when the power is applied, but this is not remotely true. Generating what is usually called a "power on reset" can be done in various ways, but usually a dedicated power management chip is used.