How to install a bootable ISO onto a single partition of a usb stick?
You can use Unetbootin to copy the Linux ISO to 1.2GB partition(disk4s3).

If I were you though I would first rewrite the partition type as GPT instead of APM by running:

diskutil partitionDisk disk4 GPT fat32 Linux 10% ExFat d2 10% ExFat d3 80%


Then select the Linux partition on disk4 in UNetbootin to be the destination for the ISO copy.