LED display flickering when connected to an ESP8266
Your schematic design has some missing components. you need to have input EMC filters close to USB connector. you also need a 2.2uF electrolytic decoupler capacitor at the regulator output and a 100nF low ESR cap at its input for stability.
Unlike it seems easy but Voltage regulators must be designed with lots of care otherwise they could be unstable. (look at related Steve Sandler's articles)

But the flicker effect that you have on the LEDs is very similar to unwanted EMI effect at the gate of MOSFET transistors inside the LED driver.

The wi-fi chip could be the source of generated EMI too therefore it need an EMI low pass filter for its power rail.

The LED driver also need bypass capacitors close to its VDD/VSS rail.

Moreover the bread board is not a good environment for solving EMC problems. you have to make a PCB and then If the problem still exist, try to solve it. Normally with a good PCB most of EMC problems will never appeared and multilayer PCBs are ten times better than single/two layer ones in tolerating EMC.

With direct power injection method you can find the most vulnerable point of your circuit and especially if the flicker repeated, you can find your weakness point and design a cure for it.