The word that best completes the sentence is "fanatical."
The completed 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" describes extreme enthusiasm or devotion, which fits the context of fans dedicated to following a team.
The other options do not fit as well:
- "Flagrant" means something that is obviously wrong or scandalous.
- "Fatuous" means silly and pointless.
- "Feline" relates to cats.
Therefore, "fanatical" is the most appropriate choice.