Coffee in Thermo flask, milk separated or mix both coffee and milk in thermo, which one is warmer?

I'm glad you explained the objective because it makes a difference. Heat loss is proportional to the difference in temperatures, inside to outside. So the coffee by itself loses heat faster than the lower temperature of the mixture. But the difference is rather small.

What is harder to tolerate is that milk put in hot coffee cooks. When you open the bottle after a while, the milk has been converted to white blobs that float on the coffee. It is still the same, but it has an unpleasant feel.