\documentclass[final]{ltugboat}

\usepackage[most]{tcolorbox}

\usepackage{varwidth}

\usepackage{mwe}

\usepackage{showframe}

​

\newlength{\mytitlelen}

​

\makeatletter

\tcbset{

  commonoptions/.style={

    enhanced, show bounding box,

    fonttitle=\bfseries\scriptsize,

    titlerule=0pt, boxrule=0pt, boxsep=0pt,

    toptitle=6pt, bottomtitle=4pt,

    opacityframe=0,

  },

  myenlargeleft/.style={

    enlarge left by=\linewidth - (\kvtcb@width)},

% width/.store in=\kvtcb@width, https://github.com/T-F-S/tcolorbox/blob/9858cec2254aab25a099d919e158a05132abab31/tex/latex/tcolorbox/tcolorbox.sty#L202

  mywidth/.code={%

    \settowidth{\mytitlelen}{\bfseries\scriptsize #1}%

    \tcbset{width=\mytitlelen+\kvtcb@lefttitle+\kvtcb@righttitle}%

  },

}

\makeatother

​

\NewTColorBox{receivedmsg}{s o m}{

  commonoptions,    

  coltitle=red, colbacktitle=yellow!30, 

    colback=yellow!30, 

  title={#3},

  IfBooleanTF={#1}{%

    mywidth={#3},  

    }{%

    hbox, varwidth upper=.8\linewidth, 

    },

   halign=flush left,

   IfValueT={#2}{#2}

}

\NewTColorBox{sentmsg}{s o m}{ 

  commonoptions,    

  halign title=flush right,

  halign=flush right,

  coltitle=blue, colbacktitle=green!30, 

  colback=green!30,  

  title={#3},

  IfBooleanTF={#1}{%

    mywidth={#3},  

    }{%

    hbox, varwidth upper=.8\linewidth, 

    },

  IfValueT={#2}{#2},

  myenlargeleft,

 }    

\begin{document}

\blindtext

\begin{receivedmsg}{Tostin:}

  You know, I spent a lot of years disliking women. But I don't dislike you.

\end{receivedmsg}

\begin{sentmsg}*{Edna:}

  Oh?

\end{sentmsg}

\begin{receivedmsg}{Tostin:}

  You're not a woman. You're more than a woman. You're a \emph{mechanic}.

\end{receivedmsg}

\begin{sentmsg}{Edna:}

  Half line length

\end{sentmsg}

\begin{sentmsg}{Edna:}

  I would like this to be flush right.

  I would like this to be flush right.

\end{sentmsg}

\begin{receivedmsg}*{Tostin:}

  Y

\end{receivedmsg}

\begin{receivedmsg}{Tostin:}

  Half line length

\end{receivedmsg}

\blindtext

\begin{receivedmsg}{Tostin:}

  You know, I spent a lot of years disliking women. But I don't dislike you.

\end{receivedmsg}

\begin{sentmsg}*{Edna:}

  Oh?

\end{sentmsg}

\begin{receivedmsg}{Tostin:}

  You're not a woman. You're more than a woman. You're a \emph{mechanic}.

\end{receivedmsg}

\begin{sentmsg}{Edna:}

  Half line length

\end{sentmsg}

\begin{sentmsg}{Edna:}

  \flushright How to have this effect without explicitly using \cs{flusright} in the box text?

\end{sentmsg}

\begin{receivedmsg}*{Tostin:}

  Y

\end{receivedmsg}

\begin{receivedmsg}{Tostin:}

  Half line length

\end{receivedmsg}

\blindtext

\end{document}