maybe the milk is thinning the stock down to much. Try adding the milk with the stock and thicken with the flour and water. I think of Chicken and Noodles as a thin and Chicken and Dumplings (biscuits) as thicker.

Try this, make a roux with just butter and flour, make sure there are no lumps and it should be smooth. slowly add your stock so that you won't get flour lumps, let that thicken, then add your milk, again slowly. whisking/stiring the whole time. If your gravy still isn't the texture you want make a cornstarch slurry, its just cornstarch and water. Add that a little at a time and that should thicken it. A slurry doesn't have exact measurements, its just put cornstarch in a bowl and water till its dissolved, it doesn't take a whole lot of water.... hope this helps... :)

I like my soups thick, more stew like. I add instant mashed potatoes too.

Like some that have posted I always start with a roux, but have never used cornstarch as a roux but regular white flour.
The more that you brown your roux it lessens the thickening power howver...learned that from Emeril Lagase. I dont brown my roux but cook for 1 full minute to remove raw taste.
When I make my cream soups Iuse stock, to make the gravy but finish off with half and half or full on heavy cream. Have used plain milk in a pinch.
Thanks for the hint on rice flour...i'll give that a try.

Make a roux with just butter (or drippings) and flour. No cornstarch. Cook until the desired color. Then add milk for cream gravy or broth to add to soups and stews. Shouldn't break down at all. Mine never does.

Try not using any cornstarch - it doesn't hold the thicken agent I have found I stick just with flour.

I would not add flour AND cornstarch. Old-fashioned gravy is made with flour. As some have described, add some flour to the fat left in the pan, brown it, then slowly add water while whisking. I prefer to use watered down cream for that step.

If you choose to use cornstarch, as I do - because I am gluten intolerant, as someone mentioned, mix the cornstarch with COLD water, then whisk it into your broth. Bring it to a boil until it thickens.

Either way, if you cook it too long, or on high temp., the fat will separate from the broth and you'll have
a watery mess.

My DH can't have Gluten. So I make all gravy out of either rice flour or potato flour. Works great for me. Never have a problem with it staying thick.

I've had that happen with cornstarch, but never with flour. You can also use Arrowroot.

I use cornstarch and water. Thicken it till it's like a paste and add.