Does a candle burn without gravity?

No a candle doesn’t burn in gravity. Once lit the hot air will not rise and the flame will become starved of oxygen. However some flames are possible and NASA spent a long time and a lot of money studying their shapes in order to make spacecraft safe.

In the absence of gravity – i.e. no up or down – then the flame shape becomes spherical and the flame needs to rely on diffusion to get oxygen to the combustion zone – the place in the flame where the chemical reactions take place. Diffusion is generally much slower and less efficient that convection.