Read stdin stream in a batch file

set /p doesn't work with pipes, it takes one (randomly) line from the input.
But you can use more inside of an for-loop.

@echo off
setlocal
for /F "tokens=*" %%a in ('more') do (
  echo #%%a
)

But this fails with lines beginning with a semicolon (as the FOR-LOOP-standard of eol is ;).
And it can't read empty lines.
But with findstr you can solve this too, it prefix each line with the linenumber, so you never get empty lines.
And then the prefix is removed to the first colon.

@echo off
setlocal DisableDelayedExpansion

for /F "tokens=*" %%a in ('findstr /n "^"') do (
  set "line=%%a"
  setlocal EnableDelayedExpansion
  set "line=!line:*:=!"
  echo(!line!
  endlocal
)

Alternatively, on some environments (like WinRE) that don't include findstr, an alternative with find.exe might suffice. find will accept a null search string "", and allows search inversion. This would allow something like this:

@echo off
setlocal DisableDelayedExpansion

for /F "tokens=*" %%a in ('find /v ""') do (
  ...

FOR /F "tokens=1* delims=]" %%A IN ('FIND /N /V ""') DO (
    >  CON    ECHO.%%B
    >> %File% ECHO.%%B
)

Source here: http://www.robvanderwoude.com/unixports.php#TEE

The set "line=!line:*:=!" syntax is:

1. set requires one parameter that is a=b.
   If a contains a space or something, you'll have to use the quotation marks around this parameter. Here I don't see any

2. !line:*:=!
   For this syntax, you can type 'set /?' to see the official description on using variables.
   !var! is like %var%, to get the value. But !var! means delayed expansion.

line var name

the first : variable modification mark.

**:= **:=(empty), replace the string in the variable's value matches "*:"(virtually from the string start to first : occurence) with (empty), i.e. delete the substring from start to first colon.