How long do fishes survive in a milk environment?
I can't support this answer with scholarly articles. But it's an interesting question if you think of milk as highly polluted water.

Water from a tap (which is what goldfish usually live in) is 'fairly pure', with the naturally occurring minerals sodium, calcium, magnesium and potassium respectively in highest concentrations (varies by location.)

Milk, on the other hand, has not only a much higher mineral content, but also has fat, protein, carbohydrates, and white blood cells as 'pollutants'. In fact, whole cow's milk is only ~87.8% water. 

Looking at calcium alone, the concentration of Ca in water is about  3 mg per 100cc, or .003%. Milk has .13% Ca, or 130 mg per 100cc. Since Ca is a major player in nerve and muscle function (in humans, a very relatively mild increase in serum Ca causes tetanic contraction of muscle), my guess is that the poor little fish would not be able to maintain normal serum Ca levels for long. It would die of inability to move fluid over its gills, that is, it would suffocate even in the presence of dissolved oxygen. Not to mention that the gills would also be coated to some extent by fat (3.5%), protein (3.8%) and other 'gunk'.

How long would it last? Probably not more than a few minutes.