But to be safe, the clock line should link to the daisy chain in reverse order, meaning the clock line goes first to the last chip in the chain, and then successively to the others, and finally to the first chip. That means the existing output value of any chip is clocked into the next chip before it has a chance to change. The propagation delay is probably enough to cover this anyway, but why not buy the insurance. Of course that means no fanout of the clock signal - it should go to the last chip, then to the penultimate chip, then ..., and finally to the first chip (the chip that gets the data input from the MCU).
+1 on making sure the clock line is properly driven, and terminated if necessary.