Hi Tim.
My now five year old had a white food aversion for a long time,but fortunately all my kids drink milk.He just decided at 5 "I'm 5 now I like..." and started trying new things,so refusing it now doesn't mean forever.
Do you and his Mum drink milk,eat ice cream around him,so he can see it's nice and everyone else is having some..I'd avoid the you have to drink that/you need to drink that approach and see if the less attention paid to the issue,it suddenly becomes forgotten.With my eldest daughter she refused fruit,but I kept just giving a little but saying nothing,and at some point it disappeared.
As for amounts,300ml,about two glasses of milk is enough for ages 1-3,according to the Food Standards gency.You can also get it from breakfast cereals,bread,pulses,soya,tofu,beans,some fish.Dark green veg,some dried fruit.I know it's not ideal but what about milkshakes or even Nesquik(not ideal I know but if it works ).Encourage the fromage frais,what about custard,I've coloured that before or added cocoa powder just so it's not white.I also use a small tin of evaporated milk when I make jelly.
My kids rarely eat eggs as eggs but we put them in pancakes,waffles,cakes,quiches,eggy bread,lots of ways to hide them.
I'm not a big fan of artificial vitamins,I think it's better if you can get what you need from your diet,but if you are worried your son may be not getting what he needs that may be helpful also.
Hoping it's just a phase