Extracting amplitudes of components from FFT
Once you use parabolic or other interpolation for a frequency peak location estimate, you can use an offset Sinc kernel, centered at that estimated frequency, to interpolate the magnitude of that peak location.  Sum each of the complex components of all the adjacent component values of the FFT result that are above the local noise floor (weighted by the offset Sinc kernel).  Then take the magnitude of that complex result.

If you use any window function (other than rectangular of FFT width) use the transform of that window function instead of a Sinc kernel.