How to animate an element that move along a path in Beamer?

For the sake of beauty, the flow chart itself should be drawn with TikZ as well. This comes with the bonus that all node coordinates are readily available for positioning a dot on the connecting lines.

What follows is an animate(-package)-based solution. The flow chart with its static objects is saved in a box first and then re-used in the animation. (Using package xsavebox for size-effective storage.) Click for viewing it in action.

documentclass{standalone}

usepackage{tikz}
usetikzlibrary{shapes}
usepackage{animate}
usepackage{xsavebox}

tikzset{dot/.pic={fill[red] (0,0) circle [radius=2pt];}}

begin{document}

% save flow chart
begin{xlrbox}{Flow}
  begin{tikzpicture}[every node/.style=draw, -latex]
    useasboundingbox (-0.6,-1.5) rectangle (3,1.5);
    path (0,1) node [rounded rectangle] (start) {Start}
          (2,0) node [trapezium, trapezium left angle=60, trapezium right angle=-60] (hello) {Hello!}
          (0,-1) node [rounded rectangle] (end) {End};
    draw (start) -| (hello);
    draw (hello) |- (end);
  end{tikzpicture}
end{xlrbox}%
%
% dot moving along node connections
begin{animateinline}[controls={play,stop}]{12}%
  multiframe{11}{rPos=0+0.1}{%
    begin{tikzpicture}
      node [anchor=south west, inner sep=0pt] at (-0.6,-1.5) {theFlow};
      path (start) -| (hello) pic [pos=rPos] {dot};
    end{tikzpicture}%
  }%  
  newframe* % pause here, click to continue
  multiframe{11}{rPos=0+0.1}{%
    begin{tikzpicture}
      node [anchor=south west, inner sep=0pt] at (-0.6,-1.5) {theFlow};
      path (hello) |- (end) pic [pos=rPos] {dot};
    end{tikzpicture}%
  }%  
end{animateinline}

end{document}

If, however, an external graphic with a flow chart is to be used, the connection line's start and end coordinates must be manually determined and then inserted by means of TikZ's coordinate command. Putting a grid with help lines on top of the node with the embedded graphic might help in this process.

Here we make use of the callouts package to put coordinates and to annotate the external flow chart with the animated red dot. Helper lines are temporarily inserted with helpgrid[gray]. The number of frames of each animation section should be adjusted with respect to the individual lengths of the connection lines in order to achieve a well-balanced speed of the moving dot. Again, click to see the animation in action.

%documentclass[dvisvgm]{standalone} % dvilualatex example ; dvisvgm --exact --font-format=woff2 --zoom=-1 example 
documentclass{standalone}

usepackage{animate}
usepackage{callouts}
usepackage{xsavebox}

tikzset{dot/.pic={fill[red] (0,0) circle [radius=3pt];}}

begin{document}

% save flow chart
begin{xlrbox}{Flow}
  begin{annotate}{includegraphics{N5Zfy}}{1.0}
    helpgrid[gray]
    coordinate (plan route east) at (-6.85,-2.05);
    coordinate (route west) at (-6,-2.05);
    coordinate (route north) at (-4.7,-1.3);
    coordinate (don't know west) at (-2.75,3.9);
  end{annotate}
end{xlrbox}%
%
% dot moving along node connections
begin{animateinline}[controls={play,stop}]{12}%
  multiframe{6}{rPos=0+0.2}{%
    begin{annotate}{theFlow}{1.0}
      path (plan route east) -- (route west) pic [pos=rPos] {dot};
    end{annotate}
  }%  
  newframe* % pause here, click to continue
  multiframe{41}{rPos=0+0.025}{%
    begin{annotate}{theFlow}{1.0}
      path (route north) |- (don't know west) pic [pos=rPos] {dot};
    end{annotate}
  }%  
end{animateinline}

end{document}