The word that best completes the sentence is "fanatical."
The sentence would read: "Some of the team's fans were fanatical and spent incredible amounts of time and money following them around the country."
The word "fanatical" describes someone who is extremely passionate and enthusiastic about something, which fits the context of fans who dedicate large amounts of time and resources to support their team.
The other options do not fit the context:
- "flagrant" means obviously offensive or disgraceful.
- "feline" relates to cats.
- "fatuous" means silly and pointless.
Thus, "fanatical" is the most appropriate choice.