Only one Flag.
When capturing another player's flag, you only get one flag. It doesn't matter how many they have, you still only get one.
> If you have a person as a Secret Pal either through StreetPass or Passing By online, when you talk to them in their base if that player has collected flags today, you will be able to receive an amount of flags equal to the amount they have collected, up to 30 per player.
That is the only way to get multiple flags from one Secret Base.