From The TimeSplitters Wiki

Flame Tag Glitch
Requirements	Flametag
Finder	Nevar00

In the Flame Tag game mode in TimeSplitters 2, there is a glitch that sometimes, if you kill an Al Bots, it will not come back to life. This is usually followed by three scenerios. Either

1 The person will still be able to be caught on fire and will need the fire transfered from them to a character still playing

2 The person will die while on fire and will stay on fire and the fire can not be transfered

3 The person will die not on fire and will not be able to be caught on fire

This glitch is most likely the reason that flame tag did not appear in TimeSplitters Future Perfect, as it the only game mode to appear in TimeSplitters 2 and not in TimeSplitters Future Perfect.