Create zip file and ignore directory structure

Using -j won't work along with the -r option.
So the work-around for it can be this:

cd path/to/parent/dir/;
zip -r complete/path/to/name.zip ./* ;
cd -;

Or in-line version

cd path/to/parent/dir/ && zip -r complete/path/to/name.zip ./* && cd -

you can direct the output to /dev/null if you don't want the cd - output to appear on screen

Somewhat related - I was looking for a solution to do the same for directories. Unfortunately the -j option does not work for this :(

Here is a good solution on how to get it done: https://superuser.com/questions/119649/avoid-unwanted-path-in-zip-file

Use the -j option:

   -j     Store  just the name of a saved file (junk the path), and do not
          store directory names. By default, zip will store the full  path
          (relative to the current path).

You can use -j.

-j
--junk-paths
          Store just the name of a saved file (junk the path), and do  not
          store  directory names. By default, zip will store the full path
          (relative to the current directory).