For jpg's, no they will not get smaller. Maybe even a smidge bigger if you zip them. Usually not enough to make a practical difference.

Zip does generic lossless compression, meaning it can be extracted for a bit-perfect copy of the original. Very simplified it works by finding patterns repeating and replacing a long pattern with a short key, and storing an index to replace the keys with the original pattern on extraction.

Jpg's use lossy compression, meaning some detail is lost and can never be reproduced. Jpg is highly optimized to only drop details that don't matter much for human perception of the image.

Since jpg is already compressed, there will not be any repeating patterns (duplicate information) for the zip algorithm to find.

For images it may be better but images are already compressed so there may not be a large saving in zipping them.

Alternative options would be to use more storage efficient formats like webp for instance.