How do I indent the 2nd line a long chapter name created using the tocloft package so that it lines up correctly?

There are numerous problems with the code you posted, which will explain why the titles don't line up.

Specifically:

\renewcommand{\cftchapfont}{ } % this should not have a space

it should be

\renewcommand{\cftchapfont}{} % notice there is no space here

The following command:

\renewcommand{\cftchapaftersnumb}{\phantom{CHAPTER}\rm} 

is a hack for spacing. It should be removed altogether.

Another extra space in:

\renewcommand{\cftchappagefont}{ }    % this should not have a space either

should be

\renewcommand{\cftchappagefont}{}

You can specify the width of the chapter number and the text will wrap appropriately. So adding your commands to a minimal document, you get the following:

\documentclass{book}
\usepackage{tocloft}

\begin{document}
\renewcommand{\cftbeforechapskip}{\baselineskip}      % allow spacing after each chapter/section entry
\renewcommand{\contentsname}{TABLE OF CONTENTS}
\renewcommand{\cftbeforetoctitleskip}{-0.25in}        % Title is 1in from top
\renewcommand{\cftaftertoctitleskip}{2.0\baselineskip}% 1 double space after title
\renewcommand{\cfttoctitlefont}{\hfill}               % Blank space before title
\renewcommand{\cftaftertoctitle}{\hfill}              % Blank space after title
\renewcommand{\cftchapfont}{}                         % Can make it bold faced here; don't put a space in the {}
\renewcommand{\cftchapleader}{\cftdotfill{\cftchapdotsep}}
\renewcommand{\cftchapdotsep}{\cftdotsep}             % Puts dots after chapter entries
\renewcommand{\cftchappresnum}{CHAPTER\ }             %
\renewcommand{\cftchapaftersnum}{}                    % Don't put a space in the {}
\renewcommand{\cftsecleader}{\cftdotfill{\cftsecdotsep}}%
\renewcommand{\cftchappagefont}{}                      %
\renewcommand{\cftchapnumwidth}{1in}
\frontmatter
\tableofcontents

\mainmatter
\chapter{A really long chapter heading that will wrap around in the table of contents}
\section{First section}
\section{Second section}
\chapter{Another chapter}
\section{Another section}
\end{document}