In my project, there is a BillboardGui above each player for their nickname. However, I’ve noticed that on mobile devices, such as my phone, the GUIs seems to flicker, where as on my laptop, I haven’t seen a case of it before.
I’m not sure if I can see the flickering in this picture, but try making the AlwaysOnTop property of the BillboardGui set to true. This may help your situation if what’s happening is what I think is happening.