Macbook Pro 2015's screen flashes up and down

Basically the image on the display would randomly flash to some point below on the screen, then flash back to it's normal position, and so on. This flashing happens as soon as the apple logo is displayed at startup, and applies even to the dead battery logo.

This is a hardware issue - it's likely the LCD or back light is damaged in some way. If you're seeing this on startup that means it's happening prior to software being (fully) loaded.

... a few days ago it was dropped on the floor.

That would be the cause. I've seen this (well variations of this) numerous times. The best way to confirm this is to "remove" the LCD from the equation - plug in an external monitor. If there's no flashing there, it's the LCD.

Fix

You need to replace the LCD. It may be the back light, but I doubt it. You'll need an LCD Assembly. iFixit.com has an excellent step by step guide on replacing it. If this is not your cup of tea, I definitely recommend taking/sending it in for repair. You may need to source this from eBay or similar to get the best price - these run in the $4-600 (USD) price range