You don't need to do this conversion. Most pudding mixes don't contain dry milk. And the mixture is in there to provide starch, not anything else.
The first and best way to make a cake is to start with a good existing recipe. Getting a substitution right is not trivial, it requires some theoretical knowledge and a few iterations of making the recipe and comparing it side-by-side. It can taste OK the first time, but a tested recipe will taste great from the first time, without giving you trouble. Moreover, this one has been converted from normal ingredients to substitutions for some reason. Back-converting it is unnecessary.
If you are absolutely decided to go with this recipe and make the substitution, you can use cake flour. Forget the pudding and its extraneous milk and sugar, and calculate the gluten content of your cake if made with cake flour (use roughly 10% for AP flour, 0% for pudding powder and whatever percentage is printed on your cake flour package, typically 6-7%). If replacing all the flour with cake flour does it, that's best. If the ratio is off, calculate how much pure starch to add to AP or cake flour to get the gluten amount right while keeping the total flour amount constant (which is the weight of your flour + the weight of the pudding from the original recipe).
If you think the original pudding made a difference in fat content, just use cream instead of the liquid milk. The more fat and less water you have in a recipe, the more cakelike it becomes, the most common types of cake use no water or dairy at all. Milk makes your cake more quickbread like. And if that's the effect you want, don't bother replacing anything there just because there might or might not have been dry milk in the author's pudding mix.
