You are nesting tikzpicture, which one should not do. To avoid it, you can use a savebox. As for your question, you can then simply use xscale=-1.
\documentclass{article}
\usepackage{tikz,blindtext}
\input{inkscape.tex}
\newsavebox\Ornament
\savebox\Ornament{\ornament{scale=1}}
\title{Table 1}
\author{}
\begin{document}
\maketitle
\begin{tikzpicture}[remember picture,overlay]
\node[below left] at ([xshift=-1cm,yshift=-1cm]current page.north east)
{\usebox\Ornament};
\end{tikzpicture}
\begin{tikzpicture}[remember picture,overlay]
\node[below left,xscale=-1] at ([xshift=1cm,yshift=-1cm]current page.north west)
{\usebox\Ornament};
\end{tikzpicture}
\blindtext
\end{document}

A neat side-effect of this is that the coordinates are now symmetric [xshift=-1cm,yshift=-1cm] vs.[xshift=1cm,yshift=-1cm]`, and it is easy to avoid the overlap.
\documentclass{article}
\usepackage{tikz,blindtext}
\input{inkscape.tex}
\newsavebox\Ornament
\savebox\Ornament{\ornament{scale=1}}
\title{Table 1}
\author{}
\begin{document}
\maketitle
\begin{tikzpicture}[remember picture,overlay]
\node[below left] at ([xshift=-0.25cm,yshift=-1cm]current page.north east)
{\usebox\Ornament};
\end{tikzpicture}
\begin{tikzpicture}[remember picture,overlay]
\node[below left,xscale=-1] at ([xshift=0.25cm,yshift=-1cm]current page.north west)
{\usebox\Ornament};
\end{tikzpicture}
\blindtext
\end{document}

\reflectboxand\rotatebox, but one should really not nest tikzpictures. – Aug 06 '18 at 14:16tikz:D But will keep that in mind :) – Raaja_is_at_topanswers.xyz Aug 06 '18 at 14:18