Creatures your opponents control have base power and toughness 0/1 until end of turn.
Flatline affects only creatures your opponents control at the time it resolves. Creatures they begin to control later in the turn won't change power and toughness.
Flatline overwrites any effects that set a creature's power and toughness. Any existing effects or counters that raise, lower, or switch a creature's power and/or toughness continue to apply to the creature's newly-set power and toughness.