In American English, we don't (to my knowledge) ever say "milk coffee." We say "coffee" (on the understanding that you are free to add milk to it if you please, just like you are free to add sugar but we don't then call it "sugar coffee"), or "coffee with milk" (or cream, of course).
Just to add to the confusion, there is also "coffee milk", which is almost all milk with just enough coffee to give it a hint of coffee flavor. Some would say this is a description of many Starbucks drinks, but I'm talking about a homemade concoction.
In my AE usage in this kind of usage, milky would always be a negative description for something watered down (not necessarily with milk), but also, not even blended completely; also, it would mean drab, nondescript, in terms of paint colors so improperly mixed they have taken on a dreary tinge of mud.
In a more general context "spiritless" or "hazy" (as though watered down with milk).
There are government regulations as to what may be called "milk chocolate", and if we choose to believe Wiki the EU and the USA have differing definitions of milk chocolate: [from Wiki]... The U.S. Government requires a 10% concentration of chocolate liquor. EU regulations specify a minimum of 25% cocoa solids. However, an agreement was reached in 2000 that allowed what by exception from these regulations is called "milk chocolate" in the UK, Ireland, and Malta, containing only 20% cocoa solids, to be traded as "family milk chocolate" elsewhere in the European Union...
I have never heard the term "milky chocolate" or "milky coffee". It sounds vaguely reminiscent of baby-talk.