Tornado,
We're making the assumption here that the flask will contain an alcoholic beverage.
FAA regulations list alocholic beverages as a hazardous material. You can take up to 5 liters onboard if the alcohol content is between 24% and 70% and if it is in a retail bottle. Alcohol less than 24% is not considered a hazardous material and more than 70% alcohol is banned.
Your flask full of booze is illegal. Your flask empty is fine. Your flask with something non-alcoholic is going to get looked at as if it is a gasoline filled Molotov Cocktail and you may be strip-searched! OK, I'm probably joking about the strip search part. Probably.
Most airlines also have policies that ban an open container of alcohol being brought onboard to protect their own in-flight sales. Assuming you have made it through this far without being arrested (or strip searched) you will now have to face an angry flight attendant on the last leg of a 14 hour long work day!
Depending on your reaction, you could now be interfering with crew operations, you could meet an Air Marshall at an inopportune time (with his knee in the back of your head as you lay on the floor), and they could divert the flight and hand you over to the FBI and sue you for the diversion costs.
All this chain reaction could happen just because of a little flask.
Throw the flask away before you get in any more trouble, bring $5 for a drink on the flight, and remember, exact change is appreciated by the flight attendants!