That is partially true - Flasks DO get you drunk immediately after drinking one, but the first one you drink only gives you one minute toward the Drunkard title.
The first Spiked Eggnog you drink, on the other hand, automatically gives you three minutes towards the drunkard title.
Just a warning for you aspiring Drunkards out there that were looking to score some Spiked Eggnog equivalents this weekend...
