I'm far from an expert in Buddhism, but here's my stab. It seems that like much between Buddhism and Christianity, there is certainly overlap between with respect to Annica and Anatta and the Christian concept of matter and souls, but there is also disagreement.
The idea of impermanence is largely shared by most Christian traditions and Buddhism, although some of the details will be different. As an example many Christians are reminded at the beginning of Lent that they are "dust and to dust you will return," which seems very similar to the idea of the absence of permanence described by Annica. It also reminds me very much of the Benedictine idea that our station in life, current assignment, and all that entails are material life is liable to change at any moment, and must be met with a certain detachment.
Some Christian traditions have aspects that would disagree with parts of Annica. Take, as an example, the idea of angels: these are conditional beings (in the sense that their existence continues only because God allows it), but they exist in an eternal dimension, and therefore their stations are not changeable.
The idea of Anatta seems more complicated. In both Buddhism and Christianity, there is the idea that unwise ("unskillful" seems to be the Buddhist term) actions lead to suffering, and a large part of Anatta seems to be focusing on asking skillful questions where a person's self is not the central focus. However, one consequence of Anatta is that the question "Do I exist?" is not answerable - it is an unskillful question, which does not help alleviate suffering. In the Christian tradition, the question has a clear answer: yes, I do exist.