Sure.

Here's an argument:

Suppose there is a dichotomy of beliefs, X and Y, their probabilities are Px and Py, and the utilities of having each belief is Ux and Uy. Then, the average utility of having belief X is Px*Ux and the utility of having belief Y is Py*Uy. You "should" choose having the belief (or set of beliefs) that maximizes average utility, because having beliefs are actions and you should choose actions that maximize utility.

What is the flaw in this argument?

For me, the flaw that you should identify is that you should choose beliefs that are most likely to be true, rather than those which maximize average utility. But this is a normative argument, rather than a logical flaw in the argument.