At most alpha levels, this test would "meet significance" and allow you to reject Ho, concluding the underlying distributions are not (MV) normal (assuming this is a MV test). However, I can't recall much about the K-S test in MV applications. In univariate cases, it is often highly sensitive to immaterial departures from normality, so it's better to use graphical methods. In a multivariate setting, this is more difficult when you get to higher dimensions (which may be where a formal test comes in). If you only have 2 variables, you could simply plot the data and check for an elliptical pattern to see if MVN is reasonable. Additionally, we also know that if some variables are MVN distributed, it is necessarily true that any linear combination of the variables is normally distributed, and each variable is univariately normal. However, the converse is not necessarily true. If I recall, then, if one of the variables is not univariately normal, then the group cannot be MVN (but all being univariate normal doesn't guarantee MVN). Maybe someone can check me on that. You may want to look into other options for assessing MVN.

If this is some sort of correlation (maybe cannonical?) it seems like this may be reasonably collinear, unless I'm missing something.

As far as I know, Box's M test relies on MVN, which you concluded is violated earlier, so Box's M test is possibly not as appropriate as Levene's HOV test.

Tell us more about your data. How many DVs do you have, how many groups, what are the sample sizes in each group. These test statistics have different properties that are better suited in different situations and one or a few may be best in a given situation based on your particular project. For example, Pillai's trace is most robust w.r.t. to normality and covariances with relatively balanced designs. The rule of thumb I learned is a ratio of the largest group sample size to the smallest group sample size should not exceed 1.5.

Again, maybe someone else can comment, or correct some of my replies, but I think you should tell us more about your project and also consider some of the replies I've given about your approach.