Simple steps:
1) Use a flask.
2) Get 1-59 minutes of use from the flask. This can be used on it's remaining seconds of use.
3) Use a second flask of the same type.
4) The buff will increase to 2 hours and will last for 2 FULL hours effectively giving you an hour of free flask.
By default most timers go to 2h visually, yes - but this timer actually does last two hours. Try it. After a little over an hour the timer will drop down to 59 minutes.
Something seems to have gotten mixed up when they changed it in 5.4. Another note; I've only tested this with Flask of the Warm Sun.