Extracting amplitude of signal from FFT plot
This looks rather similar to this MATLAB example. The maximum of the FFT plot is the estimated amplitude (perhaps with a scaling factor). 

Note the ~10% error in the amplitude estimation of the 120Hz signal- not coincidentally it's higher by the noise floor. Perhaps you can estimate the noise floor if it's reasonably flat in your case and subtract it to get a better estimate. More samples will also help, but at 1Hz it may take quite a long time.