For an 8:15am flight will arriving at 6:35 on the metro allow enough time to get to checked in at British Airways?
It should be enough time but if you're uncertain you can take the Airport Express Bus, X95 from alongside Syntagma Square earlier. It will take about 45 minutes to reach the airport at that early hour. The bus costs €3.2 and leaves Syntagma every 20-30 minutes, 24/7/365.
Do you mean that you will arrive at the airport at 6:35? If so, that should be fine since the metro station is right next to the airport (short walk).
But if you mean catching the metro at 6:35 to get to the airport for an 8:15 flight - then no it is not enough time. It can take 40-50 minutes on the metro.
We're planning to take the 6 am metro out of Monistraka and assume it will arrive within a few minutes of schedule. Is an hour + sufficient to get thru airport security, etc.?
The airport is small and well-designed. It's easy to find your departure gate once you've checked in, so assuming that the lines for BA aren't excessively long, one hour is enough time. But if there are lots of people it could take longer.
No, it is not early enough if 6:45am is when you take the metro. It takes almost an hour from Syntagma.