I had a problem with page flicker using Pure & Simple; tried your suggestion of 3/31/19 and a number of other things and nothing works. I am now seeing the flicker on your demo sites as well, and I wonder if there is something in your theme codes that can take care of this issue. Multiple browsers, PCs and Macs both. https://demo.styledthemes.com/?theme=Pure%20Simple https://demo.styledthemes.com/?theme=Nora
and several others.
We have a reasonable fast internet connection but it may not be as fast as yours. Perhaps there is a test you can try to see what it looks like for other people.
The page is loading for me quite fast, hardly notice any kind of flicker. You can try to do some optimization on the site, first try to move the custom css from the customizer to your child theme css file in /wp-content/themes/puresimple-child/style.css
See if that helps.
You can also try to force the logo height to be fixed so the header have a preset height and it won’t be “moving the rest of the page down” until your logo image loads fully loads, try this CSS
Is it your previous website midwestcentertherapy.com ? We don’t see any flickering issue associated to it, or if it is another one please locate it by sharing us your website url.
We don’t see any issues with our demo themes you mentioned above. We’ve tested with different sytems and browsers.
Could you also cross check if the issue is prevalant if you use other devices apart from yours?