I don't think this is good. It sounds like you have some non-dimmable bulbs on a circuit with a dimmer. That will always end badly.

I would disconnect the wires from the first fixture that started flickering and see if that solves your problem.

Do you have a dimmer or a switch? For troubleshooting, you can replace the dimmer with a simple on-off switch and see if everything works properly like that. If it does, then its a poor interaction between the dimmer and the LEDs. Not all dimmers are rated for LED's and not all LED's are dimmable. Check what you have...