How to recover value of current line spread?

The value is stored as baselinestretch. However, your code would need something additional:

letsavedbaselinestretchbaselinestretch

linespread{1}selectfont

<My stuff>

linespread{savedbaselinestretch}selectfont

The blank lines are necessary.

A better way out is to use an environment:

newenvironment{normalspread}
 {parlinespread{1}selectfont}
 {par}

begin{normalspread}
<My stuff>
end{normalspread}

However, this would leave uneven spacing around the part with linespread{1} (as would the naive code above.

A better example:

documentclass{article}
usepackage{lipsum}

newenvironment{normalspread}
 {paraddvspace{medskipamount}linespread{1}selectfont}
 {par}

linespread{1.5}

begin{document}

lipsum[1][1-6]

begin{normalspread}
lipsum[2]
end{normalspread}

lipsum[3][1-6]

end{document}

but the spacing has been added “by eye”.

Something better can be obtained with setspace.

documentclass{article}
usepackage{setspace}
usepackage{lipsum}

onehalfspacing

begin{document}

lipsum[1][1-6]

begin{singlespace}
lipsum[2]
end{singlespace}

lipsum[3][1-6]

end{document}