You have to do some chasing in kpfonts.sty to arrive at
\documentclass{article}
\DeclareSymbolFont{largesymbolsA}{U}{jkpexa}{m}{n}
\SetSymbolFont{largesymbolsA}{bold}{U}{jkpexa}{bx}{n}
\DeclareMathSymbol{\varprod}{\mathop}{largesymbolsA}{16}
\begin{document}
\[
\varprod_{i=1}^n A_i\ne\prod_{i=1}^n A_i
\]
\end{document}

The steps
Look for \varprod in kpfonts.sty; this shows the third code line above
\re@DeclareMathSymbol{\varprod}{\mathop}{largesymbolsA}{16}
(the re@ part must be removed)
Look for the definition of largesymbolsA which leads to the other two lines of code
\DeclareSymbolFont{largesymbolsA}{U}{jkp\kp@famillem exa}{m}{n}
\SetSymbolFont{largesymbolsA}{bold}{U}{jkp\kp@famillem exa}{bx}{n}
Finding what \kp@famillem means, but it's used for supplying an l if the light fonts are requested, otherwise it does nothing.
\ifkp@lightmath
\def\kp@famillem{l}
\else
\def\kp@famillem{}
\fi
Test.
Hurray!