Having issues with clocking a 74S374 (D Flip Flop)
The 74S374 is a bipolar TTL part.  Bipolar TTL inputs source current, so must be pulled low by a very low value resistor, or more often a switch to ground, to guarnantee that the input will be seen as a Low.  An open (unconnected) input will usually be seen as a logic High, but it is good practice to use a pull-up resistor to ensure that the input will be seen as High.

If you leave the clock input open, it will be seen as a High, and connecting it to Vcc will just make it Higher - it will never be Low, so no Low->High transition to clock the flip-flops.