Which phylum appeared most recently
In my view, we simply don't have good enough data to answer this question. The fossil evidence is too sparse prior to the Cambrian and the evidence that we do have suggests that the phyla were already too separated. Meanwhile, the depth of time and the different lifecycles and circumstances of the species involved mean that any "genetic clocks" we might use are likely to be too poor at keeping time and, indeed, different attempts have delivered different estimates of the time of divergence.