Let's start with the difference of malted and unmalted and what flaked is.
Malted is the process to allow a seed to begin germination then stopped when the seed has a specific amount of enzymes, sugars and starches.
Unmalted In the state of a raw dried seed there are no enzymes or sugar, just starches.
Flaked, Rolled This process runs grain between two hot rollers to dry and flatten the grain exposing endosperm. The hot process denatures enzymes.
So the only difference between malted and unmalted flaked grains is the sugar starch ratio.
When using oats as an adjuct for mouth feel, body and head. Really what your going for are those starches and so it makes little difference in malted or unmalted. It really depends on how they are added in the brew process.
When using as a significant part of your fermentables. The level of malting or modification determines if you need to do a cereal mash or not, to unlock (gelatinize) the starches. So mash enzymes can convert them to sugars.
Basically you can get the same results with both malted and unmalted with different brewing methods.
For examples: You can get the starches from both unmalted and malted oats by steeping them post mash.
You can also get both to produce fermentables by adding a cereal mash step for unmalted / under modified oats. Using malted or highly modified oats (instant oats) these can skip the cereal mash. The level of the malting / modification determines how much fermentables or starches will come out of the mash.