The first thing you should check is whether you're using a dimmer on those circuits, because cheap LEDs flicker like crazy with a lot of dimmers, even if the installation is brand new. If you don't have a dimmer, the next step is to swap out those LED bulbs for ones from a known brand (Philips, Ledvance, something decent quality) and see if the flickering goes away. If you change the LEDs and it fixes it, then that's your answer: it was the bulbs. If it keeps happening even with new LEDs, then something's wrong with that installation.
Since you tested them on another circuit and they still flicker, rule out that it's a problem with that specific cable. What could actually be happening is your installation has some kind of loose connection issue in the junction box or at the switch, which causes voltage fluctuations. Sometimes a loose connection isn't obvious at first glance. It's worth opening up your distribution box and checking that all the connection screws are tight, especially the neutral wire - that's the most common culprit for flickering. Also check your switches: if you tighten them and the flickering drops or disappears, that's your problem right there.
If none of this works, you could measure the voltage at those outlets with a multimeter to see if it's stable (should be around 230V with no fluctuations) or just call an electrician to check it out with proper equipment. But my guess is it's either cheap LEDs or a loose connection on the neutral wire.