Managing a project: separate .tex-files, externalized TikZ, folders

You can try something along this:

In main.tex:

\documentclass{book}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize
\def\useexternalfile#1{\tikzsetnextfilename{#1-output}\input{\csname tikzexternal@filenameprefix\endcsname#1.tikz}}
\begin{document}

\tikzsetexternalprefix{./chapter1/tikz/}
\include{chapter1}

\tikzsetexternalprefix{./chapter2/tikz/}
\include{chapter2}

\end{document}

EDIT: A cleaner, more LaTeX-y definition of \useexternalfile would be

\makeatletter
\newcommand{\useexternalfile}[1]{%
    \tikzsetnextfilename{#1-output}%
    \input{\tikzexternal@filenameprefix#1.tikz}}
\makeatother

For the record, \tikzexternal@filenameprefix is the internal macro where \tikzsetexternalprefix saves the "current prefix". Also, you can substitute #1-output for your favourite expression (maybe generated-figure-#1?)

END EDIT

In chapter1.tex:

... 
\begin{figure}
\useexternalfile{myfigure}
\caption{...}
\end{figure}
...

In chapter1/tikz/myfigure.tikz:

\begin{tikzpicture}
\draw (0,0) rectangle (4,4);
\end{tikzpicture}

(I tested this in my OSX system and it works; I use something slightly simpler). This differs from your question in that myfigure-output.pdf lives in folder chapter1/tikz/ and not in chapter1/ as you seem to want. Perhaps you (or others) can tweak it a bit more.