Use the direct selection tool, pick the point that’s at the end of the flame, then on the stroke settings window, increase your Mitre Limit. Value will depend on your lines and they way they curve, so keep cranking it up until you get what your looking for.
<Rove>What the...?<\Rove>
Direct selection on one point? Mitre limit will affect the whole object. You dont need to select one point with DS Tool, just select the whole object with the Selection Tool? Using the DS Tool on one point would be a time waster (and just think what you could do with all those seconds you have saved ;-)).
Mitre limit is sketchy at best. You will never get all objects to have nice pointy bits just how you want them with it.