First of all, I would like to recommend you to not use \tikzstyle to define your styles in favor of \tikzset (for further information see Should \tikzset or \tikzstyle be used to define TikZ styles?).
Another remark: I noticed you used both \draw and \path; actually, \draw is a shortcut for \path[draw] thus, as your style line already contains the key draw, there's not difference in using one or the other one. Notice: only in case both exploit the line style.
Also, the connections can be drawn much more easily thanks to a loop: indeed, most of the lines of code are identical.
Said that, the straight way to solve the problem is to use the library calc, which helps in defining a commodity coordinate useful to draw the paths.
\documentclass{report}
\usepackage{tikz}
\definecolor{arm}{RGB}{100,140,171}
\usetikzlibrary{arrows,calc,positioning,shapes.geometric}
\begin{document}
\pagestyle{empty}
\begin{figure} [htbp]
\hspace{-1.9cm}
\resizebox{!}{7.5cm}{
\begin{tikzpicture}[node distance = 1.5cm, auto,>=stealth]
\tikzset{los/.style={diamond, draw,fill=arm,text width=3em, text badly centered, text=white, node distance=3cm, inner sep=0pt}}
\tikzset{quadri/.style={rectangle, draw, fill=arm, text width=6em, text centered,text=white , rounded corners, minimum height=2.5em}}
\tikzset{line/.style={draw, thick, color=black, -latex'}}
\node[quadri] (A) {A};
\node[quadri, below of=A, node distance=1.6cm] (B) {B};
\node[quadri, below left=1cm and 2cm of B ] (C) {C};
\node[los, below of=C , node distance=2.2cm] (D) {D};
\node[quadri,below left=1cm and 1.6cm of D] (E) {E};
\node[quadri,below of=E, node distance=1.6cm](F) {F};
\node[quadri,below of=D, node distance=1.97cm](G) {G };
\node[quadri,below of=G, node distance=1.6cm](H) {H};
\node[quadri,below right=1cm and 1.6cm of D] (I) {I};
\node[quadri,below of=I, node distance=1.6cm](J) {J};
\node[quadri, below right=1cm and 2cm of B ] (K) {K};
\node[quadri,below left=1.3cm and 0.22cm of K] (L) {L};
\node[quadri,below of=L,node distance=1.6cm] (M) {M};
\node[los,below right of=K,node distance=3cm] (O) {O};
\node[quadri,below left=1cm and 0.05cm of O](P){P};
\node[quadri,below of=P, node distance=1.6cm](Q) {Q};
\node[quadri,below right=1cm and 0.05cm of O](R){R};
\node[quadri,below of=R, node distance=1.6cm](S) {S};
\node[quadri,right of=A ,node distance=3.5cm](T) {T};
\node[quadri, text width=7em,right of=T ,node distance=3.4cm](U){U};
\foreach \source/\dest in {
A/T,T/U,A/B,B/C,B/K,C/D,E/F,G/H,I/J,K/L,K/O,
L/M,P/Q,R/S}{
\path [line] (\source) -- (\dest);
}
\path [line] (D) -| node [near start,above] {$=0$} (E);
\path [line] (D) -- node[right] {$=1$} (G);
\path [line] (D) -| node [near start,above] {$=0$} (I);
\path [line] (O) -| node [near start,above] {$=1$} (P);
\path [line] (O) -| node [near start,above] {$>1$} (R);
% useful coordinate:
% it is defined as half way between S and Q shifted
% below of 1 cm
\coordinate (below scheme) at ($(S)!0.5!(Q)-(0,1)$);
% path from U to the south of the scheme
\path [line,-] (U.east) -- ($(U.east)+(1.5,0)$) |- (below scheme); % I used again the style line, but - removes the arrow that in this case should not be deployed
\path [line] (S|-below scheme)--(S);
\path [line] (below scheme)-|(M);
\end{tikzpicture}
}
\caption{Flowchart}
\label{fig:flowchart}
\end{figure}
\end{document}
The result:
If your aim is to connect all the leaves of the tree, you might exploit a different solution:
% = = = = = = = = = = = = = = = = = = = =
% THIS IS TO CONNECT U TO all
% = = = = = = = = = = = = = = = = = = = =
\coordinate (below scheme) at ($(F)-(0,1)$);
\path [line,-] (U.east) -- ($(U.east)+(1.5,0)$) |- (below scheme); % I used again the style line, but - removes the arrow that in this case should not be deployed
\foreach \module in {F,H,J,M,Q,S}
\path [line] (\module|-below scheme)--(\module);
The snippet should replace:
% useful coordinate:
% it is defined as half way between S and Q shifted
% below of 1 cm
\coordinate (below scheme) at ($(S)!0.5!(Q)-(0,1)$);
% path from U to the south of the scheme
\path [line,-] (U.east) -- ($(U.east)+(1.5,0)$) |- (below scheme); % I used again the style line, but - removes the arrow that in this case should not be deployed
\path [line] (S|-below scheme)--(S);
\path [line] (below scheme)-|(M);
in the previous document.
The new code defines the commodity coordinate (below scheme) to be 1cm south of F. Now, by exploiting the ability of the calc library to compute intersections, each arrow is defined as a path starting from module |- below scheme towards module. Please refer to the pgfmanual for further information on the calc library.
This provides you:
Best Answer
Not the final picture, but it includes all the elements you want, I think.