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." This word implies an extreme and uncritical enthusiasm, which fits with the context of devoted fans.
The other options do not fit the context as well:
- "fatuous" means silly or foolish, which doesn’t convey the dedication implied.
- "feline" relates to cats, which is irrelevant here.
- "flagrant" means something that is shocking or outrageously bad, not applicable to the positive connotation of devoted fans.
Thus, "fanatical" is the correct choice.