From Bulbapedia, the community-driven Pokémon encyclopedia.
Flow is a property that is determined by the weaknesses and resistances of the types of Pokémon inside of the Purification Chamber.
In each sub-chamber, up to four Pokémon can be arranged around the Shadow Pokémon being purified. Placing a Pokémon whose type is super effective against one of the next Pokémon's types, clockwise around, will result in high flow. A type that inflicts normal damage results in weaker flow, one that is resisted will be weaker still, and one with no effect will be the weakest. Because the Template:Type2 is not super effective against any other type, it is treated as super effective against itself in the Purification Chamber.
Flow is one of the most important things about the organization of Pokémon inside of the sub-chambers. High flow among Pokémon in a group of four will raise the tempo of the music inside the chamber, causing the Shadow Pokémon in the middle to be purified very quickly, while a low flow will purify Pokémon at a rate similar to just walking around with the Pokémon in the party.
Having a high flow, and thus a high tempo, among all nine of the sub-chambers in the Purification Chamber is the only way to purify Shadow Lugia.