At one time Area 51 added all the sites' reputation. But it is not the case now if I am not mistaken. My reputation in Area 51 (in Health Proposal) is 1,447:
But my flair from Stack Exchange, for today, shows 1.3k:
Why is this the case?
Area 51 normally shows the reputation in all your sites (where the reputation is at least 200), under "total rep"; what shown under the link to your Area 51 profile is more complicated.
Take as example this user. That user's reputation is shown as in the following screenshot:
Brad Koch's reputation on Stack Overflow is 392, and that is the only site where his reputation is at least 200. 548 is the sum of the reputation on Stack Overflow, and Area 51.
This user doesn't have a reputation of at least 200 on any site, but Area 51 reports his reputation as in the following screenshot.
The shown reputation is not 0. In this case, I am not able to understand which SE sites are considered. The sum of reputation in all the sites where the user has an account, including where the reputation is lower than 200, is 402. I cannot find three numbers between 108, 95, 85, 63, and 51 whose sum is 212; the closer I can get is 222 (108+63+51), but I cannot understand in which way those three numbers are chosen. The numbers I summed are the reputation of Area 51, and two sites with the older accounts created by the user (2 years ago). Maybe the difference can be explained from the fact the data is cached.