Graphically clipping three copies of the word works, but requires manual adjustment of the position of the clip start/end:

(based on egreg's answer at Character with two colors)
MWE
\documentclass[12pt]{article}
\usepackage{xcolor}
\usepackage{trimclip}
\usepackage[voc]{arabxetex}
\setmainfont{Al Qalam Quran Majeed Web}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.1]{AlQalamQuranMajeedWeb}
\definecolor{Kalkola}{HTML}{EE171F} %
\definecolor{Kalkolab}{HTML}{12AF1F} %
%\newcommand{\kal}{\color{Kalkola}}%
\begin{document}
{\Huge\begin{arab}
\mbox{%
\textcolor{Kalkolab}{\clipbox{0 0 {0.7\width} 0}{sub".ha"A}}%
\textcolor{Kalkola}{\clipbox{{0.3\width} 0 {0.5\width} 0}{sub".ha"A}}%
\textcolor{Kalkolab}{\clipbox{{0.5\width} 0 0 0}{sub".ha"A}}%
}
sub".ha"A
\end{arab}
}
\end{document}
Added
Adapting a Tikz solution (also using clipping) from the same linked question is also possible and easier conceptually but more intricate coding-wise, and the resulting Tikzpicture needs to be boxed to flow right-to-left with the text (an \mbox will do), and needs to be lowered vertically by a small amount in relation to the baseline (here, with \raisebox and a negative amount).

MWE
\documentclass[12pt]{article}
\usepackage{xcolor}
%\usepackage{trimclip}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage[voc]{arabxetex}
\setmainfont{Al Qalam Quran Majeed Web}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.1]{AlQalamQuranMajeedWeb}
\definecolor{Kalkola}{HTML}{EE171F} %
\definecolor{Kalkolab}{HTML}{12AF1F} %
%\newcommand{\kal}{\color{Kalkola}}%
\newcommand{\Atwo}[3][A]{%
\begin{tikzpicture}
%place the underlying word
\node[inner sep=0pt,outer sep=0pt,text=#2] (a) {#1};
%define the clip rectangle
\clip (a.south east) [xshift=-1ex] rectangle (a.north);
% place the clipped word above
\node[inner sep=0pt,outer sep=0pt,text=#3] {#1};
\end{tikzpicture}
}
\begin{document}
{\Huge\begin{arab}
\fbox{sub".ha"A} {\raisebox{-.482ex}{\fbox{\Atwo[sub".ha"A]{Kalkolab}{Kalkola}}}} sub".ha"A sub".ha"A
sub".ha"A sub".ha"A {\raisebox{-.482ex}{{\Atwo[sub".ha"A]{Kalkolab}{Kalkola}}}}
sub".ha"A
\end{arab}
}
\end{document}