Well, I have never seen the loot been reduced because of flasks. Your titan loot solely depends on your rank and what loot tier you end up at. So suppose you end up at loot tiers 9-13, you will always get 3 Ascension Material rolls (see here). I have never seen that being reduced because of flasks.
But, if you are saying that using flasks reduces the chance of getting unfarmable AMs, then honestly speaking there is no data available to support this claim.
Titan loot is based on the Loot tier you get (XI, X, IV, VII etc …) which is in turn based on the damage you dealt and the number of stars your titan is.
In truth, the more flasks you use, the higher your rank will be so better loot should be gotten (Getting A rank compared to C rank)
I’m running a titan loot data project to pin down the odds of getting various items and materials from titans. In this post I also link to an explanation of the titan tiers and ranks etc…