@SMEAS solution worked for me.

Looking at docs it seems we've used the incorrect particle system to have GPU instancing enabled.
docs.unity3d.com/Manual/PartSysInstancing.html
"The particle shader that supports GPU instancing is called Particles/Standard Surface."

Unfortunately I don't have the skills to make a shader of this type to verify if it works properly. If our art team gets to implementing this I'll edit.

@SMEAS solution also worked for me.
looking at docs https://docs.unity3d.com/Manual/PartSysInstancing.html it seems we were using the wrong particle system to have GPU instancing enabled:
"The particle shader that supports GPU instancing is called Particles/Standard Surface."

Unfortunately I don't have the skills to create one to see if it actually works with GPU instancing enabled and doesn't flicker. Will edit if our art team implements this and it works.

Still happening in 2022.1.17f1 on Android in VR and URP

2022.2.17f1!

not fixed on Android builds with 2022.1.17f1

Can confirm, 2022.1.0b13 has fixed for built-in too :)
Thank you!

I am hoping too that this is fixed for built in as well, this is not just specific to urp

Just to make sure, the fixes will cover the built-in pipeline as well?
Tickets that have been marked as "duplicate" of this one, are referring to the built-in pipeline too.

Also indeed the issue is related to GPU instancing somehow as I can confirm what SMEAS said.

In my case I was able to get rid of the flickering by disabling GPU Instacing on the particle system.