This is a fascinating question, let's divide it into three parts, 1) is there Kehuna after death 2) if there is is readind a Cohen's Tora first included in "V'Kidashto" 3) Halacho L'Maaseh

1) There is a huge discussion amongst the Achronim if there is Kedushas Kehuna after the Cohen passes away. This would be germane Halacha l'Ma'aseh if there are two people requiring burial at the same time. Harav Chaim Kanyevsky Ztz"l states unequivocally the there is no Kedushas Kehuna after death. Rebbe Akiva Eiger Ztz"l implies that there is Kedushas Kehuna after death. From the limited research I have done, there are more opinions that there is not Kedushas Kehuna after death, but it is not clear that this is a definitive conclusion in Halacha.

2) I have no proof, but from my personal Svara I would say that when there is an action of Kedusha to be performed (to make a bracha) or some bestowing of pleasure that increases the prestige of the honored one (to take the first portion at a Seudah) one must let the Cohen perform that action first. However, when learning the Sefer of the Acharon, I am doing the learning in the Sefer that is already published, and therefor even if there is Kedushas Kehuna it is irrelevant to V'Kidashto.

3) Halacha L'Maaseh, the custom is indeed to learn the Shach before the Taz. I don't think it has anything with the fact that the Shach was a Cohen. I assume that the reason is that in general the Halach is like the Shach and therefore it makes more sense to learn the Shach first.

Shimon Brodie