Wrapfigure two figures left and right with text in between

Another solution, using the insbox plain TeX macro package: it defines \InsertBoxL and InsertBoxR commands with two mandatory arguments: the number of lines unshortened in the following paragraph, before the insertion of the box, and the content of the box, and a last optional argument, the number of supplementary shortened lines, in case TeX has erroneously calculated the height of the inserted box. Of course, the inserted objects are no more floating, so you have to use \captionof{figure}{some caption}.

\documentclass{article}
\usepackage[latin]{babel} 
\usepackage{lipsum}
\usepackage{graphicx,caption} 
\input{insbox}
\makeatletter
\@InsertBoxMargin=3mm
\makeatother

\begin{document}

\InsertBoxL{0}{%
\parbox{0.5\textwidth}{
\includegraphics[width=0.45\textwidth ]{AliceSteadman}
\captionof{figure}{Ralph Steadman’s cover for Alice in Wonderland}
}}[10]
\lipsum[1]

{\InsertBoxR{6}{%
\parbox{0.4\textwidth}{
\includegraphics[width=0.4\textwidth ]{traccia-table}
\captionof{figure}{Meret Oppenheim Table with bird legs (1972)}
}}[7]
\lipsum[1-2]}
\lipsum

\end{document} 

Will this serve the purpose?

\documentclass{article}
\usepackage{tikz}
\usepackage{lipsum}
\usepackage{multicol,caption}
\newenvironment{Figure}
{\par\medskip\noindent\minipage{\linewidth}}
{\endminipage\par\medskip}

\begin{document}
    \begin{multicols}{2}
        \begin{Figure}
            \begin{tikzpicture}
            \draw (1,1) circle (3cm);
            \end{tikzpicture}
            \captionof{figure}{text}
        \end{Figure}
        \lipsum[2]
    \end{multicols}
    \begin{multicols}{2}
        \lipsum[2]
        \begin{Figure}
            \begin{tikzpicture}
            \draw (1,1) circle (3cm);
            \end{tikzpicture}
            \captionof{figure}{text}
        \end{Figure}
    \end{multicols}
\end{document}

I have not used wrapfigure here, but multicols can also serve something similar. I agree that this is not a good solution for you if you want to continue using wrapfigure environment.

You can do it with wrapfig, so long as you make sure the first wrapfig is done before starting another. \wrapfill adds blank lines (actually, paragraphs) until this point is reached.

Note, always use \parskip=0pt with wrapfig.

\documentclass{article}
\usepackage{wrapfig}
\usepackage{graphicx}
\usepackage{lipsum}

\newcommand{\wrapfill}{\par\ifnum\value{WF@wrappedlines}>0
  \addtocounter{WF@wrappedlines}{-1}%
  \null\vspace{\arabic{WF@wrappedlines}\baselineskip}%
  \WFclear
\fi}

\begin{document}

\begin{wrapfigure}{L}{0.5\textwidth}
\includegraphics[width=\linewidth]{example-image-a}
\caption{Image 1}
\end{wrapfigure}

Really long text to be on the right of image 1...
\arabic{WF@wrappedlines}
\wrapfill

\begin{wrapfigure}{R}{0.40\textwidth}
\includegraphics[width=\linewidth]{example-image-b}
\caption{Image 2}
\end{wrapfigure}

Really long text to be on the left of image 2...
\wrapfill

At this point the bottom wrapfigure is done.

\end{document}