It is a little difficult to tell just what you are trying to do so I'm not sure this is what you are looking for. However, you do say that you want the text printed "on top of" the picture. I'm not sure if this means above the picture or over the picture.
This code puts the picture under the text so that the text is printed on top of the picture. That is, the picture forms a background. The text is printed on the background.
\documentclass[a4paper,11pt,draft]{memoir}
\pagestyle{empty}
\usepackage{flowfram}
\usepackage{graphicx}
\usepackage{tikz}
% left frame
\newflowframe{0.2\textwidth}{\textheight}{0pt}{0pt}[left]
\newlength{\LeftMainSep}
\setlength{\LeftMainSep}{0.2\textwidth}
\addtolength{\LeftMainSep}{2\columnsep}
% right frame
\newflowframe{0.7\textwidth}{\textheight}{\LeftMainSep}{0pt}[main01]
\begin{document}
\begin{tikzpicture}[remember picture, overlay, x=4cm, y=20cm]
\node at (0,0) {\includegraphics[width=4cm,height=20cm]{symbol_strip.jpg}};
\end{tikzpicture}
\begin{figure}
\begin{flushright}
\vspace{-2cm}
Tractor beat trailer give backwoods hee-haw gold frogskin plumb nugget. Liniment fancy rightly work chicken what cipherin' how ya. Heapin' backwoods her hospitality em got creosote overalls rodeo up. Townfolk soap out.
\end{flushright}
\end{figure}
\end{document}
Note that I used the draft option to quell errors about not finding the image. This produces this:

I'm not sure why you have made this a figure. If you want things positioned precisely, you don't want TeX moving them around and that's what the figure environment tells it to do!
EDIT (DELETION):
Based on your edited question, I assume you don't want the text above the image. Since this pushed stuff off the page, I'm deleting this part of my original answer.
EDIT (UPDATE BASED ON UPDATED QUESTION):
Based on the image you posted, you might try something like the following but replacing the tikzpicture with the background image you have on hand.
\documentclass[a4paper,11pt,final]{memoir}
\pagestyle{empty}
\usepackage{flowfram}
\usepackage{graphicx}% not needed to produce my demo
\usepackage{xcolor}% not needed if you use a background image
\usepackage{tikz}
% left frame - alternatively, specify a larger proportion of \textwidth or set this width absolutely
\newflowframe{0.2\paperwidth}{\textheight}{0pt}{0pt}[left]
\newlength{\LeftMainSep}
\setlength{\LeftMainSep}{0.2\paperwidth}
\addtolength{\LeftMainSep}{2\columnsep}
% right frame - alternatively, specify a smaller proportion of \textwidth or calculate width from the absolute width of the left flow frame etc.
\newflowframe{0.7\paperwidth}{\textheight}{\LeftMainSep}{0pt}[main01]
% recalculate left/right margins - or see alternatives above
\newlength{\mywidth}
\setlength{\mywidth}{\LeftMainSep}
\addtolength{\mywidth}{0.7\paperwidth}
\settypeblocksize{\textheight}{\mywidth}{*}
\begin{document}
\begin{tikzpicture}[remember picture, overlay]
\fill [fill=blue!20] (0,1cm) -- (0,-14cm) -- (4cm,-19cm) -- (4cm,1cm) -- cycle;
\end{tikzpicture}
\vfill% or set \vspace*{whatever you like}
\hspace*{\parindent}% text in specimen is set into page somewhat
\begin{minipage}[c]{3cm}% adjust to taste
\raggedleft
Tractor beat trailer give backwoods hee-haw gold frogskin plumb nugget. Liniment fancy rightly work chicken what cipherin' how ya. Heapin' backwoods her hospitality em got creosote overalls rodeo up. Townfolk soap out.
\end{minipage}
\hspace*{1em}% avoid text hitting edge of frame or background - adjust to taste
\vfill\vfill% adjust to taste or reduce to one \vfill if setting \vspace*{} to a specific value above
\framebreak% force following text to next flow frame
\section*{Sphinx of black quartz}% demonstrate relative positioning of text in next frame
Peter Piper picked a pickled pepper.
\end{document}
which produces:
Note the difference between \paperwidth and \textwidth. Unless you virtually zero the left/right margins, one fifth of the \textwidth is not enough to contain a 4cm wide image. So assuming you want something which looks roughly like the image you posted and that you don't wish to alter that image, I am guessing you want the left flow frame to be wider. I've kept the proportions the same and set the margins based on the resulting widths. So the margins are now very small. If this isn't what you want, you could increase the proportion of the page width taken by the left flow frame relative to the main one, or set the left flow frame to an absolute width (e.g. 4cm or whatever) and calculate the width of the main flow frame accordingly.
If the text should be higher up, increase the number of \vfill commands following the minipage, tweak the position of the minipage or just set the amount of vspace before the minipage to whatever you like.
Best Answer
Use the
minipage
environment: