Spend all your time working on permanent solutions to the issues of aging, death, and/or political conflict, or whatever other big issues you think are important.
Should they keep their muscles flexed 24/7?
You are using "flexing muscles" as a shorthand for something, and I don't know what. Flexing muscles to impress others is silly; you have better things to do. Flexing muscles to exercise might make some sense, but infinite willpower doesn't imply infinite ability to recuperate from exercise. Stay within the limits of your body so long as you have a use for it.
For the past few years my willpower has been steadily increasing. If it lasts and I use it to accomplish something noteworthy, I might write a post about it.
Anyway, what should a rational preference utilitarian with infinite willpower do? Assume that there are no negative effects (unhappiness, stress) with using this willpower, and that they can control their emotions at will.
Clearly they should work a lot more, not spend time on recreation (movies, TV, games), stand instead of sitting, etc..
What else? Should they listen to music? Should they keep their muscles flexed 24/7 ? What should they learn, where would they have the most relative advantage? How much time would be worth spending on social interaction?
I can figure out these things on my own, but those questions are important and good ideas are very valuable.