Power for the 8" 800x600 screen from Picade

Hi all, first post here and it’s just a bit of a query really.

I’m making a self contained RetroPie rig using the screen you guys sell and a battery pack. I’ve got one of those RavPower 16000mah power packs to power it - having strung everything together that’s needed (Pi, screen, controller, keyboard) I’m just not quite getting enough power to the screen to keep it on - it keeps starting up, then turning off. That’s fine, the screen is powered by 5v USB and the power pack has two USB outputs.

What I’m wanting to check is, what kind of current are both the Pi and the screen rated for? The power pack has one 2.1A supply and one 2.4A supply - the Pi is a Pi2, so I know it’s fine on the 2.1A supply. If I put 2.4A into it, a) would the Pi be okay, and b) would I have the extra juice to run the screen? And if not, if I plug the screen straight into the 2.4A power pack, is the screen going to be okay? There’s clearly enough juice altogether to run everything, I just don’t want to overload anything.