coding the arrow's path in flowchart

You only need to remove node "A-6" and draw arrow from A-3 to A-2. I also took opportunity in rearrange loading tikz libraries and a little bit simplified/ shortened code for image:

\documentclass[a4paper,11pt,twoside]{book}
\usepackage[a4paper,
            margin=2.5cm]{geometry}
\usepackage{amsmath, amsthm, amssymb}

\usepackage{fontspec}
\usepackage{polyglossia}
\setmainlanguage{greek}
\setromanfont{Minion Pro} %% Select your favorite font
\setotherlanguage{english}

\usepackage{tikz}
\usetikzlibrary{angles, arrows, arrows.meta,
                calc, chains,
                decorations.text, decorations.pathreplacing,
                fadings, fit, 
                patterns, positioning,
                quotes,
                shapes, shadows.blur,
                spy}

\begin{document}
\centering
    \begin{tikzpicture}[
node distance = 8mm and 4mm,
  start chain = A going below,
  base/.style = {draw, minimum width=32mm, minimum height=8mm,
                  align=center, on chain=A, join=by -Stealth},
startstop/.style = {ultra thick,double,base, rectangle, rounded corners, fill=white},
  process/.style = {ultra thick,base, rectangle, fill=white},
    io/.style = {trapezium, trapezium stretches,
                 trapezium left angle=70, trapezium right angle=110,       
                 base, ultra thick, fill=white},
  decision/.style = {ultra thick,base, diamond, fill=white},
every edge quotes/.style = {auto=right}
                        ]
  \node [startstop]       {Έναρξη};     % <-- A-1
  \node [io]              {Εισαγωγή};  
  \node [decision]        {Ερώτηση};  
  \node [io]              {Απάντηση};  
  \node [startstop]       {Τέλος};      % <-- A-5

\coordinate[above left=of A-2.east] (aux);
\draw [arrows=-Stealth]
        (A-3.east)  to  ["ναι"] ++ (1,0) |- (aux) -- (aux |- A-2.north);
\path   (A-3)       to  ["όχι"]     (A-4);
    \end{tikzpicture}
\end{document}

Edit 1: compiled by XeLaTeX engine.

Edit 2: from all libraries in your MWE are actually used only the following:

\usetikzlibrary{arrows.meta,
                chains,
                positioning,
                quotes,
                shapes
                }

I modified as little as possible your code by doing:

1. I added the every join/.style=-Stealth option that automatically draws the arrows without having to rebuild the chain.

2. I placed the node A-6 at the top right of the node A-2 without joining it to the chain, without tracing it and transforming it into a coordinate.

   \node [on chain,coordinate, above right=3mm and 20 mm of A-2]{}; % <-- A-6

3. Thus, I build an arrow for the loop because (A-6) is not joined to the chain. \draw [arrows=-Stealth] (A-3) -| node[pos=.25,below]{Κάτι}(A-6)-| (A-2.30);
4. I only place the label without drawing anything more since the arrows have already been built by the chain. \path (A-3) --node[left]{όχι} (A-4);

\documentclass[a4paper,11pt,twoside]{book}
\usepackage[a4paper,left=2.5cm,right=2.5cm,top=2.5cm,bottom=2.5cm]{geometry}
\usepackage{amsmath, amsthm, amssymb, amsfonts}
\usepackage[utf8]{inputenc}
%\usepackage[greek]{babel}

% babel dont work for me, i took these 5 lines from the answer of Zarko
\usepackage{fontspec}
\usepackage{polyglossia}
\setmainlanguage{greek}
\setromanfont{Minion Pro} %% Select your favourite font
\setotherlanguage{english}

\usepackage{tikz}
% shapes
\usetikzlibrary{shapes}
%arrows
\usetikzlibrary{arrows,arrows.meta}
%decorations
\usetikzlibrary{decorations.text,decorations.pathreplacing,patterns,shadows.blur,fadings}
% miscellaneous
\usetikzlibrary{calc,quotes,positioning,fpu,angles,fit,spy,chains}

\begin{document}

    \begin{tikzpicture}[
  node distance = 8mm and 16mm,
  start chain = A going below,
  base/.style = {draw, minimum width=32mm, minimum height=8mm,
    align=center, on chain=A,join},
  startstop/.style = {ultra thick,double,base, rectangle, rounded corners, fill=white},
  process/.style = {ultra thick,base, rectangle, fill=white},
  io/.style = {ultra thick,base, trapezium, 
    trapezium left angle=70, trapezium right angle=110,
    fill=white},
  decision/.style = {ultra thick,base, diamond, fill=white},
  every edge quotes/.style = {auto=right},
  every join/.style=-Stealth]
  ]
  \node [startstop]       {Έναρξη};     % <-- A-1
  \node [io]              {Εισαγωγή}; %A-2
  \node [decision]        {Ερώτηση}; %Α-3
  \node [io]              {Απάντηση}; %A-4
  \node [startstop]       {Τέλος};      % <-- A-5
  \node [on chain,coordinate, above right=3mm and 20 mm of A-2]{};     % <-- A-6

  \draw [arrows=-Stealth] 
  (A-3) -| node[pos=.25,below]{Κάτι}(A-6)-| (A-2.30);
  \draw  (A-3) --node[left]{όχι} (A-4);
  \end{tikzpicture}
\end{document}