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As you said, a "\" after "|" does not make a functional difference.
Is your searchstring.out file okay?
Look at it with an editor on Unix.
Not created from WinDOS that appends invisible ^M (CR)...

No, j is a variable.
The whole outer loop is fed from searchstring.out, see the redirection at the end!

The inner loop is fed from the find command. The | conects the find command with the loop.

A second error is
for k in match.out ;You certainly want
for k in `cat match.out`like you did in the outer loop.
But this is not ideal for many reasons. A more efficient and less risky version:...

The * must be evaluated by the find command, you must escape it from the shell.
find / -name \*$j\*
where the $j is still evaluated by the shell. If this is not wanted, use a " " escape.
find /...