The lighting in the main space of my apartment is 6 downlights all connected to the same switch, with a dimmer. I realised fairly quickly that I couldn't have bulbs in all 6 downlight fixtures at once, because there's flickering and some fixtures don't work at all.
But: the problem was not any individual fixture, it only occurred when I had bulbs in more than 4 of the fixtures at one time.
I tried various kinds of LED bulbs, different wattages, different combinations of fixtures, and could not find a solution. So I just took bulbs out of 2 of the fixtures, left the wires dangling, and decided to wait for the day when I can eventually afford to hire an electrician to look at things.
A couple of weeks ago, I decided to try one last internet search, and discovered something unexpected.
Compared to incandescent bulbs, LED bulbs draw so little power that they sometimes cause problems with older dimmer switches. Those older dimmers are designed to handle higher power draws and can't cope with the lower draw of the LEDs, causing flickering etc.
The recommended fix is: replace the dimmer switch and all the wiring. Which is not something I can do myself (it's illegal in Australia to do your own electrical work if you're not a licensed electrician), and would be a lot harder than just replacing the bulbs anyway.
Most places in Australia only sell LED downlight bulbs these days, but I hunted around and found an online retailer that would sell me 6 incandescent downlight bulbs. Pricier than LED bulbs and they'll use more power, but I decided to give it a try.
It worked! For the first time in 18 months, all my lighting fixtures have bulbs in them, and I can dim them, and it's lovely.