Significance of steps involved in flipping process of an image?
Looking at the effect you have achieved; namely a flip along the horizontal and vertical axes, all you need is to apply steps 2,3, and 4. 

The following MATLAB / OCTAVE code would also generate the same flipped image in 3 steps as would given by your 5 step procedure:

% I is the image data
If = fft2(I);             % S1 - Take DFT2 of the real image
Gf = conj( If ) ;         % S2 - Take conjugate of DFT of image
g  = real( ifft2(Gf));    % S3 - Invert back into spatial domain

figure,subplot(2,1,1)
imshow(I);
subplot(2,1,2)
imshow(g);


The flipping result can be seen from the following symmetry property of DTFT / DFT :

$$f[n,m] \leftrightarrow F(\omega_1,\omega_2) \implies f^*[-n,-m] \leftrightarrow F^*(\omega_1,\omega_2) $$

For real data $f^*[-n,-m] = f[-n,-m]$.