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."
"Fanatical" refers to being extremely enthusiastic or obsessed, which fits the context of devoted fans.
The other options do not fit the context:
- "Fatuous" means silly or pointless.
- "Feline" relates to cats.
- "Flagrant" refers to something conspicuously bad or offensive.
Therefore, the correct answer is "fanatical."