Is publishing in your university journal considered a conflict of interest?
In academics, conflicts of interest are generally thought of as conflicts that involve monetary issues. The fact that a publication may contribute to an author getting a promotion or tenure is not considered a conflict of interest. That said, if the university owns a stake in the idea being published, there could be monetary benefits to both the university and author. Authors, however, need to disclose their conflicts of interest, and it this case, they would be expected to mention that the parent company of the publisher also has a conflict of interest.

In these cases, as in all cases, it would be left to the reader to decide how to interpret the results and conclusions. It is worth noting that most editors (regardless of if they are at the same university as the university owned publisher) have a fair amount of autonomy from the publisher and if forced to publish something they disagree with, would likely leave in a vocal manner. Similarly, peer reviewers provide another independent form of input (although they can obviously be overruled).