You said you want to "trash the entire file system and start again with a fresh install".
If that's really what you want, read on.
First thing to do:
BACK UP THE EXISTING DRIVE.
(not much more to say about that)
I recommend CarbonCopyCloner, free to download and use for 30 days.
Next thing:
Boot from the USB flash drive.
Note: I've never owned a fusion drive. Things -might- work differently than the following. If I'm wrong, hopefully others will jump in to correct me.
After that:
Open disk utility.
Is there a "view" menu?
If there is, go to it and choose "show all devices" (important).
If there IS NOT a view menu, don't worry about this, go on to next step.
Next step:
Click on the line on the left that represents the "fused" drive. I'm not sure how this is presented to the user (in disk utility) on a fusion drive Mac. It might be "the top line", or it might not be.
Now, click the erase button.
You need to specify the file format you want (you didn't tell us which version of the OS you use, that's important information).
Since the fusion drive is created from two individual drives, I'm going to GUESS that you want to "erase" the "fused volume", rather than the two individual drives, without "destroying" the fusion that bonds them together. But again, that's just a guess on my part.
If it's High Sierra or earlier, I believe you want "Mac OS extended with journaling enabled, GUID partition format".
If it's Mojave or later, I think you want "APFS with GUID partition format".
Then, erase the drive.
When that's done:
Open the OS installer and start clicking through.
Be aware the Mac may restart one or more times, and the screen may "go black on you" and stay that way for a few minutes before proceeding.
Be patient.
When finished, you should see the initial start screen "Choose your language".
Begin clicking through.
At the appropriate moment, setup assistant will ask if you wish to migrate from another drive.
If you do, connect the backup and give setup assistant time to digest things.
Then choose what you wish to migrate and let setup assistant do its thing.
It will take a while, again... be patient.
When done, you should see your account login screen.