Your battery pack is designed to be a portable battery charger for phones... Even though it is rated as "3 amps", that spec is probably the maximum amperage that it provides, which may only be when the battery is close to fully charged and at an ideal temperature. As the charge drops the amperage may drop.

Raspberry forums seem to say a 3 amp power supply is a minimum...and keep in mind a power adapter plugged into the wall can provide a steady amperage. So you might consider getting a battery that is rated to provide maybe 4 amps.

You might consider getting a USB power meter such as https://www.amazon.com/dp/B07X3HST7V which you would insert between your battery and Raspberry. Periodically look at the the voltage level and make a note about the voltage level when the flickering starts to occur. And maybe compare that level to the level shown when plugged into the wall.

The other thing to consider is maybe your battery pack is only able to deliver a total of 3 amps across both USB ports combined. In that case you might have to use one battery pack for your screen and another one for the raspberry.

(One thing you might consider before buying anything is to lower your Raspberry's clock speed and the screen refresh rate, and see if that helps.)