For the uninitiated, Shaman King Flowers takes place 16 years after the events of the main Shaman King manga and is focused on Hana Asakura, Yoh and Ana's son who inherited his father's guardian ghost, Amidamaru and his Futsunomitama no Tsurugi. A complete opposite of his father, he was chosen by the current Shaman King, his uncle Hao as the leader of his team in the "Flower of Maize", a battle between gods.
Shaman King Zero on the other hand, are a series of short stories that take place prior to the events of the series.
[Source: Anime News Network]