How to scale the amplitude of an FFT of a chirp signal
First, thanks for all your inputs. I did some research and I found my mistake. The spectrum of a linear chirp can, according to Wikipedia (search for: "chirp spectrum wiki") be analytical described in the frequency domain. The formula for the amplitude



gave me the hint. I just used the constant factor and a factor of samplingfrequency/numberofsamples to match the FFT. I do not know exactly why, but it seems to fit. 

Following Picture shows the result:



Following code can be used to simulate it:

    %% Test script
close all
clear all
clc
% create timevector
L =1000 ;
aux = 0:1:(L)-1;  % indexvector
% get fs
fs = 1000;
% create timevector
t = (1/fs)*aux;
f0 = 1;
f1 = 100;
% chirp in timedomain
SignalChirp = chirp(t,f0,max(t),f1);
% Window length
nfft= length(SignalChirp);
%generate the vector of frequencies
halfn = floor(nfft / 2)+1;
deltaf = 1 / ( nfft / fs);
ffft = (0:(halfn-1)) * deltaf;
% perform FFT
X = fft(SignalChirp,nfft);
magni1(1) = abs(X(1)) ./ (nfft);
magni1(2:(halfn-1)) = abs(X(2:(halfn-1))) ./ (nfft / 2);
magni1(halfn) = abs(X(halfn)) ./ (nfft);

figure(1)
subplot(2,1,1)
plot(t,SignalChirp,'k');
title(['Chirp Signal']);
xlabel('Time(s)');
ylabel('Amplitude');
subplot(2,1,2)
plot(ffft,magni1),hold on
duration = max(t);
c = (fs/L);
% https://en.wikipedia.org/wiki/Chirp_spectrum
scalingLinChirp = sqrt(duration/((f1-f0)));
plot(ffft,ones([length(ffft) 1])*scalingLinChirp*c), hold on
xlabel('Freq(Hz)');
legend('FFT Result' ,'Calculated Amplitude' )
ylabel('Amplitude');


If I use this scale factor to my FFT of my accelerometer data it matches the calculated theory much better than before. Sadly I can’t show you guys another picture due my low rep. 

Thanks for all your Inputs!