I'm using iPhone 7+ with matte protector. Took a week but used to it now, can use for long periods without issue. 8+ would work also but this one was free. 
Current best phones as of January 2020?
Samsung A40 with OLED saver, blue filter and glass protector (not matt) - is the only phone that is OK for me.
Samsung A70 and Pixel 3aXL are ok for me, with some time to get used it in the beginning (>2weeks).
OLED saver and any blue filter for some reason make the display worse for my eyes.
4 days later
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Looking at an iPhone 8+ right now, dithering patterns on this phone are quite noticeable to me. Do you guys notice it, and if so, does it bother you? I do remember when I owned this phone in the past the matte protector makes them less visible and overall the output looks more stable with the protector on.
5 days later
13 days later
Iphone 5 and 6 with a cheap non original screen replacement. I don't know why it works, but it works. I would like to try a screen replacemnt with a new version of iphone, but im scared to damage an expensive phone.
20 days later
degen I didn’t see your post until now, sorry about that. Anyway, no, the 8+ doesn’t hurt my eyes at all. The XR, 11, X, XS, 11 Pro all kill my eyes due to PWM on the OLED and something else on the LCD that I can’t figure out.
What’s strange is that there are people who have no issues with the XR and 11, but DO have issues with the 8+. It’s so weird that certain screens can affect people so vastly differently 
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Doing very well with the Mate 20 Pro. Use OnePlus 3 at home when maximal comfort is desired, but the battery is old and degraded. Mate 20 Pro is by far the next best thing I have tried. I think Huawei did a good job with their DC Dimming implementation, but I don't have an oscilliscope or anything to test, I just go by how I feel with it turned on vs off, and what I see on slo camera from smartphones. On the other hand their P30 was bad for me no matter what. Mate 20 Pro with the BOE panel has a very clean output.
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I have an LG G6 (android 9, may 2019 security patch) and this is fine for me, although at < 38% brightness it has PWM at about 2000hz (notebookcheck has exact figures) Initially it caused me problems if I didnt have comfort view on all the time but now I only use that at night. (had similar with Samsung S6 with screen temp issue, but that had PWM and didnt affect me) I've had the device about 3 years and its ok for me.
I've had a look at an Iphone 8+ and thats been 'ok' for me as well so I might try to pick one up 2nd hand. Even with reduce white point off this was ok while I was using it.
My work phone is a Galaxy A6 and its awful to look at, OLED with PWM at 230hz at all brightness levels. Cant use it for more than a few moments without eye pain.
PWM causes me a different sensation than the OSX / Macbook issue many seem to have. PWM hurts my eyes where as OXS (dither? etc) hurts my head and causes a painful sort of burning sensation.
The Hisense A5 will not give anyone any strain becuase it's an e-ink screen. I use it as my main phone and its great. Very functional once you learn how to set up and use it and overall a pleasure to use.
bkdo Same for me. iPhone 8+ is the best Apple device currently.
6 days later
Seanicus Well for most people yes. But people like me get eyestrain from books (yes it is crazy) and eink even more. Eink is much much better than OLED or LCD but still not perfect. Hisense s9 pro was my daily driver for over a year. I had yota 2 previously and it was a bit better.
As of today I use iPhone 7 plus with changed screen to the most cheap screen from China i could find. With original screen I would get eye strain and headaches after 10-20 s. With this bad screen I can use it for up to 1-2 minutes without any long term headaches.
If I need to read something for 10-20 mins - I use eink side of S9 pro. Not perfect, but still no long term headaches.
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Don't buy a Pixel 3a. I don't know about the XL but the normal 3a destroys my eyes and brain within minutes and leaves me with a lingering headache and the whole "I can't see properly" feeling for a while.
The PWM is disgustingly bad. The moment it's below 100% brightness it starts and by 80% it's very noticeably flickering. Honestly there's absolutely no excuse for screens flickering like this. Older OLED phones never had screens like this. I only ever saw visible flicker on OLED before the s6 when you drop the brightness to <5% and on most OLED phones there was no visible PWM at all.
The phone outside of the screen is amazing however especially for the price. I'm really disappointed I'm having to send it back because the camera is just so damn good.
On a side note one thing I've noticed is all phones I've tried which have a screen that produces a strong rainbow-esque effect when viewed from an extreme angle especially on white/lighter backgrounds always cause me eye strain and headaches much more quickly and much worse than other screens that don't produce this effect. I'm not sure if it's because of the screens sub-pixel array or a coating on the screens glass or both but this is a common theme I've found.
I've been using a Sony Xperia X compact for almost 3 years and I can use it for hours with no problem. (and Z5, Z3, etc... Before this one).
I have issues with most Samsung latest phones.
Sony Xperia XZ2. It took a couple weeks to get used, but its fine now.