I have tweaked the spacing in my scrbook table of contents using

\RedeclareSectionCommand[tocbeforeskip=1em plus 1pt]{chapter}
\RedeclareSectionCommand[tocbeforeskip=2pt]{section}
\RedeclareSectionCommand[tocbeforeskip=2pt]{subsection}


Does KOMA-Script provide a similar command for spacing in the list of figures?

You could use

\DeclareTOCStyleEntry[
beforeskip=2pt
]{default}{figure}


The size of the chapter gap between the entries in LOF and LOT can be changed by

\KOMAoptions{chapteratlists=1em}


The gap can also be disabled by listof=nochaptergap or replaced by entries for all (even if there are no figure/table) chapters by listof=chapterentry.

Example:

\documentclass{scrbook}
\RedeclareSectionCommand[tocbeforeskip=1em plus 1pt]{chapter}
\RedeclareSectionCommands[tocbeforeskip=2pt]{section,subsection}

\DeclareTOCStyleEntry[
beforeskip=2pt
]{default}{figure}
\KOMAoptions{chapteratlists=1em}

\usepackage{blindtext}% only for dummy text
\begin{document}
\tableofcontents
\listoffigures
\blinddocument

\captionof{figure}{Figure One}
\captionof{figure}{Figure Two}

\chapter{Another Chapter}

\captionof{figure}{Figure Three}
\captionof{figure}{Figure Four}
\end{document}