Do Titan flasks lower your loot?

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.