You are, in a way, manually adjusting the equations in order to get the equality sign aligned. You could then ask TikZ (or the calc package, not library) to compute the required horizontal space for you.
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{mathtools,calc}
\newcommand{\LHS}[2][1.5em]{\hspace{#1}\mathllap{#2}}
\newcommand{\RHS}[2][1.5em]{\mathrlap{#2}\hspace{#1}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
legend cell align=left,
legend columns=2,
legend style={
anchor=south,
at={([yshift=2mm]current axis.north)},%,above=0cm,left=0mm,
cells={align=center},
/tikz/every even column/.append style={column sep=5mm}
}
]
\addplot[red] {x};
\addplot[blue,domain=0:2] {x^2};
\addplot[orange] {-x};
\addplot[green] {x^3};
\addplot[green] {x^3};
\addplot[green] {x^3};
\legend{\pgfmathsetmacro{\myw}{1.5em-width("$yy$")}%
\hspace{\myw pt}text,\pgfmathsetmacro{\myw}{3em-width("$zzyyz$")}%
\hspace{\myw pt}another text,
$\LHS{yy}=x^2$,
$\LHS[3em]{zzyyz}=\RHS{x^3}$ reference,
$\LHS{k}=xyz$,
$\LHS[3em]{kk}=\RHS{xz}$ cite,
}
\end{axis}
\end{tikzpicture}
\end{document}

A perhaps more appealing output is achieved by fixing the indent, \myindent in the following MWE, and than shift the stuff accordingly. This might be the better choice even if you do not add text because then the indent will be universal.
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{mathtools,calc}
\newcommand{\LHS}[2][1.5em]{\hspace{#1}\mathllap{#2}}
\newcommand{\RHS}[2][1.5em]{\mathrlap{#2}\hspace{#1}}
\newlength\myindent
\myindent=0.5em
\begin{document}
\begin{tikzpicture}
\begin{axis}[
legend cell align=left,
legend columns=2,
legend style={
anchor=south,
at={([yshift=2mm]current axis.north)},%,above=0cm,left=0mm,
cells={align=center},
/tikz/every even column/.append style={column sep=5mm}
}
]
\addplot[red] {x};
\addplot[blue,domain=0:2] {x^2};
\addplot[orange] {-x};
\addplot[green] {x^3};
\addplot[green] {x^3};
\addplot[green] {x^3};
\legend{\hspace{\myindent}text,
\hspace{\myindent}another text,\pgfmathsetmacro{\mywleft}{\myindent+width("$yy$")}%
$\LHS[\mywleft pt]{yy}=x^2$,\pgfmathsetmacro{\mywright}{\myindent+width("$zzyyz$")}%
$\LHS[\mywright pt]{zzyyz}=\RHS{x^3}$ reference,\pgfmathsetmacro{\mywleft}{\myindent+width("$yy$")}%
$\LHS[\mywleft pt]{k}=xyz$,\pgfmathsetmacro{\mywright}{\myindent+width("$zzyyz$")}%
$\LHS[\mywright pt]{kk}=\RHS{xz}$ cite,
}
\end{axis}
\end{tikzpicture}
\end{document}

\hspace{0.5em}beforetextandanother text. – Jul 15 '18 at 12:13\LHSsome desired distance plus the width of yy or zzyyz. – Jul 15 '18 at 12:29