We will begin with the modeling of the flame

Start with a box and add some height segments

Convert to Editable Poly and adjust the mesh like this

Apply meshsmooth modifier with 1 interation

Now duplicate the object and put the copy inside the first object. It is very important that the two objects have the same pivot point and they are in the same position,
if not the next step won't work fine.

We apply strech and bend modifiers to one of the objects and instance the modifiers for the other object

For the candle, start with a cylinder, convert to Editable Poly, and deform the mesh with paint deformation. Then add the candle thread.