Yes, Kelvar does burn at the tip of a flame.
That is why you should put out the flame once the fuel has just about been all used up. Once the fuel is gone the wick starts to burn and this wears it out very fast.
The wick and stitching has to handle the heat.
Pure Kevlar can handle temperatures over 430 deg C.
Whereas Cotton will break down at 150 deg C.
In short the kevlar will burn once the fuel has gone. So put out your flames before this happens and then your stitching should last a very long time.
Also
The further you reach to the center of the flame, the lower the temperature will be.
So the tip of a flame furtherest from the wick/fuel is hottest eg 1400 deg C. (Kevlar will burn very quick here)
A few millimeters above the fuel will be cooler eg 700 deg C. and just above the fuel is much cooler again.
Below the fuel where the kevlar is will be within the 400 Deg C. Limit.
Hope that all makes sense
Malcolm