For two clocked components in series, how do you ensure that the output of the first is captured by the second

The only way I though to counter act this is to AND the flip flop's clock input with a clock that is faster than the main clock... that way data will be guaranteed to be clocked in at the end of that cycle.

This sounds to me like an architecture choice that will eventually limit the performance (maximum clock speed) you can achieve with your design. If your registers are able to function at the faster clock speed, you'll eventually want to try to get the whole system running as close to that clock speed as you can, but then you won't be able to have a "slow" clock and a "fast" clock to do this with.

In order to do this, I'm fetching data from memory, placing it on the data bus, then clocking it into a register all in a single operation. I'm worried that the rising edge of the main clock will happen at the register before the data is fetched from memory.... a sort of propagation delay / race condition.

First solution

One way that leaps to mind to solve this is to clock data out of the memory on the rising edge of the clock, and clock it in to the register on the falling edge. Since your register doesn't have a configuration bit for which edge it responds to (like it would if you were designing in an FPGA), you would have to generate the appropriate signal by using an inverter (NOT gate) between the "main" clock signal and the register.

More generally, it's possible to distribute several phases of your clock (e.g., 0, 90, 180, and 270 degrees) instead of just clock and inverted clock. And use these different phases to execute different actions at different times. Of course you have to do a fairly careful analysis of each interface where data is transferred from one phase to another to be sure setup and hold times are met.

To the best of my understanding (possibly out-of-date) multiphase clock designs were fairly common in the discrete logic design era, and were also common (and may still be common) in ASICs and custom chip designs. But they are fairly uncommon in FPGA design due to the complexity of the timing analysis.

Second solution

Another option is to create a controller state machine that enables and disables different elements on different clock cycles as needed. For example, you'd enable the memory output on cycle 1 and enable the register to latch in the data on cycle 2. Since your register apparently doesn't have a clock enable input, you might need to do this by ANDing a state machine output with the clock input to the register.

This type of design was fairly common in the era of discrete logic CPUs, and its what was taught in undergraduate digital logic courses in the early 90's. An elaborate version of this scheme is called a microcoded architecture.

Of course this architecture means that you need more than one clock cycle to complete each instruction. But it would be multiple cycles of your fast clock, not your original "slow" clock that would be used, and you are already using more than one cycle of the fast clock per instruction in your design.

You are right. Edge triggering is just a much narrower form of level triggering, and depends on timing. Inside an edge-triggered device, the changing clock edge is just turned into a pulse which causes it to accept the inputs: a level trigger! But the level trigger is very short. It must be so short that the outputs are not able to propagate back to the input to do any harm in the time that the edge-triggered pulse appears and disappears.

Edge triggering would not work if signals propagated instantly through wires and had unlimited slew rates.

Also note that clocks can be divided into phases to solve problems where this isn't fast enough.

A master-slave flip-flop is an example of clock phasing. It splits the clock signal into two phases by reacting to both rising edges and falling edges, but differently. Input is accepted on a rising edge into an input latch, and then on a falling edge propagated into a second latch where it produces output.