Here's an adjustment that should work:
set "a=%date:~10,4%-%date:~4,2%-%date:~7,2%"
set "c="
:loop
if "%c%"=="1" set "a=%a%_run "
if EXIST "C:\SeleniumGrid\Results\%a%%c%\Basic_Survey\test_output\html\Chrome\" set /a c+=1&goto loop
caution your if exist
contains test
_output
but the remaining lines you show contain test
-output
!
I'd suggest you put C:\SeleniumGrid\Results
and Basic_Survey\test?output\html\Chrome
into variables so that they can be changed easily as necessary