I notice that once I'm above 1,000,000 cookies or so, I get the flashing background. However this only happens when I click the cookie. If I don't click the cookie will it never happen? How does this affect the Elder Pledges?
Given the date of this question, it was asked before "The Big Update" which removed this issue, but moreover completely revamped the game. To play as it was at the time of the question, one can still go back to cookie clicker classic.
In the update log of cookie clicker classic, you should note that the very next day, in version 0.125, an option to disable flashing was added. To prevent flashing, simply update to the newest version of cookie clicker classic (refresh the page) or upgrade to the entirely revamped cookie clicker where this is not an issue.
According to the source code in 0.125, this will affect the elder pledge:
As noted in the if statement, turning off flashing will disable the whole of the grandmapocalypse. Also, as this is in the