This is very easy to achieve:
@echo off
for /F "delims=" %%I in ('dir * /A-D /B /O-D 2^>nul') do set "NewestFileTime=%%~tI" & goto NewestFileTime
echo There is no file in current directory.
goto :EOF
:NewestFileTime
echo Last modification time of newest file is: %NewestFileTime%
Please note date the format of date and time string assigned to environment variable NewestFileTime depends on Windows Region and Language settings as set for the used account.
There is also the possibility to get last modification time of newest file in a region independent format, see answer on Find out if file is older than 4 hours in batch file for details.
For understanding the used commands and how they work, open a command prompt window, execute there the following commands, and read entirely all help pages displayed for each command very carefully.
dir /?
echo /?
for /?
goto /?
set /?
See also Single line with multiple commands using Windows batch file for an explanation of operator & used in this batch code.