You don't need any additional software to burn a .ISO file to a USB drive, Zorin OS has what you need.
First, you have to figure out what drive is your target drive. You can do that in the Disks application, or in Terminal, you can issue: lsblk
It'll have an output like this:
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 596.2G 0 disk
├─sda1 8:1 0 512M 0 part /boot/efi
├─sda2 8:2 0 1K 0 part
├─sda5 8:5 0 2G 0 part [SWAP]
├─sda6 8:6 0 2G 0 part
└─sda7 8:7 0 591.7G 0 part
sdb 8:16 1 59.5G 0 disk
└─sdb1 8:17 1 59.5G 0 part /media/owner/STORAGE
sdc 8:32 1 29.7G 0 disk
├─sdc1 8:33 1 29.7G 0 part
└─sdc9 8:41 1 8M 0 part
sr0 11:0 1 1024M 0 rom
sda is the main internal drive, sdb is the target drive I want to burn to, sdc is the ZFS L2ARC cache drive, sr0 is the CD/DVD drive.
Now, I want to burn RescueZilla so I can create an image of the Windows installation on my new laptop, which I'll store away just in case I can't get Zorin OS to work on the new laptop. That laptop is still in the box... never been booted. I don't intend on booting it under Windows.
So again in Terminal, you'd issue:
sudo dd if=/home/owner/Desktop/rescuezilla-2.4.1-64bit.jammy.iso of=/dev/sdb conv=fdatasync status=progress
You'll note it shows the progress of the process, updating once a second.
You'll see an output like this:
2245152+0 records in
2245152+0 records out
1149517824 bytes (1.1 GB, 1.1 GiB) copied, 221.74 s, 5.2 MB/s
[EDIT]
First few tries didn't work... still working on it.
[EDIT 2]
Ah, it's a problem with RescueZilla... it won't boot. I tried Clonezilla and it boots and runs properly.