The imbiber may use a melee weapon (using melee combat modifiers) to attack flying or levitating monsters. The monster must be in the air, not just at range. Like most potions, this takes one round to drink, so the character would not be able to attack a flying monster until the round after this potion is quaffed. (a Belt of Retrieval could bypass that restriction)
It does not confer the ability to fly or levitate.