Is it possible to drink a flying potion and cast greater invisibility spell on myself (both spells would require concentration), so I can fly around invisible?
A Potion of Flying specifically doesn't require concentration.
In page 141 of the DMG under "Spells", it specifically mentions potions as an exception to the rule of concentration:
... Many items, such as potions, bypass the casting of a spell and confer the spell's effects, with their usual duration.
So, if the potion does not say it requires concentration, it's safe to assume that it doesn't. The potions listed in the DMG all say in parenthesis that they do not require concentration but your DM may invent a house-ruled potion that does require concentration, so it's still safer to ask your DM.