The flash would be coming from the loading of assets/css/images etc from the second https
url.
While http
is faster there are SEO benefits for making the public facing parts of a site https
which would solve the dual domain issue.
Prefetch
If they were on the login screen and you knew they were soon to be redirected to secure https version you could start preloading the assets on the https protocol.
Some HTML5 prefetching could be nice for that, How can I preload a page using HTML5?
<link rel="prefetch" href="/path/to/prefetch" />
link to assets consistently with https
You could link to all your assets on the http site with the https protocol, no preloading required. This might add overhead to anyone not on the https version. So you may just want to load logo/header graphics and css/js over https. This would improve the perceived performance for when the domain switched the main assets and styles would snap into place like any other reload.
CDN
Ultimate solution would be to push out the assets to a Content Delivery Network like Amazon Web Services. So both domains load the same assets, you'll have to use https
or else you'll get warnings when linking to http
when on a https
domain. When the user switches the browser will already hold a cached copy of all the assets. This will speed up page loads in general to. With the concurrent request limits browsers have (between 6 - 8) it means your server will deliver important things like HTML, and the browser can simultaneously load assets from the CDN.
SPDY
Getting back on topic, considering protocol upgrades I would start looking into Google's SPDY. Chrome Firefox Opera & IE11 have support. Its secure and faster than HTTP or HTTPS. Couple that with some WEBP graphics loading off a CDN and you'll be in danger of near light speed.
http://en.wikipedia.org/wiki/SPDY#Browser_support_and_usage