Controversies exist, but they stem more from the country than from its flag. That said, choosing the flag can itself can be controversial too.
Among a list of countries, if you list Israel, with its flag — or this one ? :-) —, this is controversial.
Displaying the flag of Palestine can be controversial too. We have an example of that here.
The flag of Tibet has been outlawed by China. In Tibet, if you own this flag, the Chinese authorities put you in jail.
According to @Dnbrv, there is a little controversy around the flag of Belarus.
Regime change in a country may need particular attention, we can see it these days. A new flag is chosen, and the old flag becomes associated with the old regime, so showing the old flag can shock and be dangerous.
Thus, Zaire has changed flag several times since its independence.
Rwanda has a new flag, and Rwanda's old flag is now associated with the regime of the genocide.
More recently, Libya abandoned the flag which was the easiest flag to draw in the world, and chose its new flag, with the star and crescent.