Is there a dutch book argument for the "independence of irrelevant alternatives" axiom? There is a dutch book argument to show that nontransitive preferences are in a sense "unreasonable", which justifies why we pose the axiom of transitivity in the definition of "rational preferences", when it comes to no-uncertainty utility. 

When it comes to utility functions over lotteries, Von Neumann and Morgenstern additionally pose the Independence axiom w.r.t. lotteries. 

Are there Dutch-book arguments to justify the independence axiom?
Yes, and it's actually quite simple. Start with alternatives {A, B}, where you prefer A to B. If there exists some C such that introducing it causes you to prefer B to A instead, then the following holds:
I start by offering {A, B}, and you take A. Then I offer C as well, and also let you trade B for A so long as you give up some arbitrarily small amount of utility denoted dx. This means that your options are {A, (B-dx), C}, where dx is some arbitrarily small amount of utility that you will lose which is chosen so as to not change your opinion that B-dx is better than A. As a result you choose B-dx instead of A. The result is that you have given up utility for no benefit -- you could originally have chosen B originally, but instead took B-dx -- i.e. that you have been Dutch booked.