To start with a quote from the beamer user guide:
Never use a smaller font size to “fit more on a frame.” Never ever use the evil option shrink.
So please use the following solution at your own risk!
\documentclass[aspectratio=169, hyperref={pdfpagelabels=false}]{beamer}
%\documentclass[handout, hyperref={pdfpagelabels=false}]{beamer}
\usetheme{Madrid}
\let\Tiny=\tiny
\usepackage{multimedia}
%\usepackage[backend=bibtex,style=authoryear]{biblatex}
\usecolortheme{whale}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[spanish]{babel}
\usefonttheme{professionalfonts}
\usenavigationsymbolstemplate{}
\setbeamertemplate{footline}[frame number]
\setbeamertemplate{frametitle}[default][center]
\setbeamersize{text margin left=2em,text margin right=2em}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage[flushleft]{threeparttable}
\usepackage{siunitx}
\begin{document}
\begin{frame}[shrink=25]{Resultados}
\centering
\begin{threeparttable}
\caption{Estimación de p$K_\text{a}$ para ácidos y alcoholes}\label{table:estimacion_pka_RM1}
\begin{tabular}{lccccc}
\toprule
& \textbf{} & \multicolumn{4}{c}{RM1} \\ \cmidrule(lr){3-6}
& & \multicolumn{2}{c}{COSMO} & \multicolumn{2}{c}{SS-COSMO} \\ \cmidrule(lr){3-4}\cmidrule(lr){5-6}
& p$K\text{a}_{\text{exp}}$\SI{298}{K} & p$K\text{a}_{\text{calc}}$ & $\Delta$p$K\text{a}$ & p$K\text{a}_{\text{calc}}$ & $\Delta$p$K\text{a}$ \\ \midrule
\textbf{Ácidos}& & & & & \\
acético & 4.75 & 2.1 & 2.6 & 4.2 & 0.6 \\
fluoroacético & 2.59 & -0.8 & 3.3 & -0.8 & 3.4 \\
fórmico & 3.75 & ref & - & ref & - \\
pirúvico & 2.39 & -3.0 & 5.4 & 0.7 & 1.7 \\
glioxílico & 3.18 & -2.3 & 5.5 & 0.4 & 2.8 \\
propanoico & 4.86 & 2.3 & 2.5 & 3.9 & 0.9 \\
butanoico & 4.83 & 2.6 & 2.3 & 4.2 & 0.7 \\
acrílico & 4.25 & 2.0 & 2.3 & 1.0 & 3.3 \\
láctico & 3.86 & 0.7 & 3.2 & 5.0 & -1.2 \\
benzoico & 4.2 & 1.1 & 3.1 & 1.6 & 2.6 \\
MAE & & & 3.1 & & 1.8 \\ \bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item {Comparación de p$K\text{a}$ calculados con RM1 y dos estrategias de solvatación: implícita (COSMO) y explícita-implícita(SS-COSMO). $\Delta$p$K\text{a}$ =p$K\text{a}_{\text{exp}}$-p$K\text{a}_{\text{calc}}$.}
\end{tablenotes}
\end{threeparttable}
\end{frame}
\end{document}

In case the font becomes too small, an alternative could be to transpose the table. Based on https://tex.stackexchange.com/a/32690/36296 a quick test:
\documentclass[aspectratio=169, hyperref={pdfpagelabels=false}]{beamer}
%\documentclass[handout, hyperref={pdfpagelabels=false}]{beamer}
\usetheme{Madrid}
\let\Tiny=\tiny
\usepackage{multimedia}
%\usepackage[backend=bibtex,style=authoryear]{biblatex}
\usecolortheme{whale}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[spanish]{babel}
\usefonttheme{professionalfonts}
\usenavigationsymbolstemplate{}
\setbeamertemplate{footline}[frame number]
\setbeamertemplate{frametitle}[default][center]
\setbeamersize{text margin left=2em,text margin right=2em}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage[flushleft]{threeparttable}
\usepackage{siunitx}
\usepackage{adjustbox}
\usepackage{array}
\newcolumntype{R}[2]{%
>{\adjustbox{angle=#1,lap=\width-(#2)}\bgroup}%
l%
<{\egroup}%
}
\newcommand*\rot{\multicolumn{1}{R{45}{0.1em}}}% no optional argument here, please!
\begin{document}
\begin{frame}[shrink=25]{Resultados}
\centering
\begin{threeparttable}
\caption{Estimación de p$K_\text{a}$ para ácidos y alcoholes}\label{table:estimacion_pka_RM1}
\begin{tabular}{lccccc}
\toprule
& \textbf{} & \multicolumn{4}{c}{RM1} \\ \cmidrule(lr){3-6}
& & \multicolumn{2}{c}{COSMO} & \multicolumn{2}{c}{SS-COSMO} \\ \cmidrule(lr){3-4}\cmidrule(lr){5-6}
& p$K\text{a}_{\text{exp}}$\SI{298}{K} & p$K\text{a}_{\text{calc}}$ & $\Delta$p$K\text{a}$ & p$K\text{a}_{\text{calc}}$ & $\Delta$p$K\text{a}$ \\ \midrule
\textbf{Ácidos}& & & & & \\
acético & 4.75 & 2.1 & 2.6 & 4.2 & 0.6 \\
fluoroacético & 2.59 & -0.8 & 3.3 & -0.8 & 3.4 \\
fórmico & 3.75 & ref & - & ref & - \\
pirúvico & 2.39 & -3.0 & 5.4 & 0.7 & 1.7 \\
glioxílico & 3.18 & -2.3 & 5.5 & 0.4 & 2.8 \\
propanoico & 4.86 & 2.3 & 2.5 & 3.9 & 0.9 \\
butanoico & 4.83 & 2.6 & 2.3 & 4.2 & 0.7 \\
acrílico & 4.25 & 2.0 & 2.3 & 1.0 & 3.3 \\
láctico & 3.86 & 0.7 & 3.2 & 5.0 & -1.2 \\
benzoico & 4.2 & 1.1 & 3.1 & 1.6 & 2.6 \\
MAE & & & 3.1 & & 1.8 \\ \bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item {Comparación de p$K\text{a}$ calculados con RM1 y dos estrategias de solvatación: implícita (COSMO) y explícita-implícita(SS-COSMO). $\Delta$p$K\text{a}$ =p$K\text{a}_{\text{exp}}$-p$K\text{a}_{\text{calc}}$.}
\end{tablenotes}
\end{threeparttable}
\end{frame}
\begin{frame}
\frametitle{{Resultados}}
\centering
\renewcommand{\tabcolsep}{0.15cm}
\renewcommand{\arraystretch}{1.2}
\begin{threeparttable}
\caption{Estimación de p$K_\text{a}$ para ácidos y alcoholes}
\begin{tabular}{lll*{11}S}
& & & \rot{acético} & \rot{fluoroacético} & \rot{fórmico} & \rot{pirúvico} & \rot{glioxílico} & \rot{propanoico} & \rot{butanoico} & \rot{acrílico} & \rot{láctico} & \rot{benzoico} & \rot{MAE}\\
\toprule
&& p$K\text{a}_{\text{exp}}$\SI{298}{K} & 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2\\[1em]
\multirow[c]{4}{*}{RM1} & \multirow[c]{2}{*}{COSMOS} & p$K\text{a}_{\text{calc}}$ & 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2\\
&& $\Delta$p$K\text{a}$ & 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2\\[1em]
& \multirow[c]{2}{*}{SS-COSMOS} & p$K\text{a}_{\text{calc}}$ & 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2\\
&& $\Delta$p$K\text{a}$ & 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2& 4.2\\
\bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item {Comparación de p$K\text{a}$ calculados con RM1 y dos estrategias de solvatación: implícita (COSMO) y explícita-implícita(SS-COSMO). $\Delta$p$K\text{a}$ =p$K\text{a}_{\text{exp}}$-p$K\text{a}_{\text{calc}}$.}
\end{tablenotes}
\end{threeparttable}
\end{frame}
\end{document}

\captionof{table}{Your caption here}
and avoid table environment (just a tabular is enough))