At this point she's swam and caught breakfast and is now sitting and drying her feathers. Anhingas (also Cormorants) don't have the natural oils most other waterfowl possess so if they try to continue to swim and dive for their food, they'll essentially get waterlogged and sink to the bottom.
As to flying...eh, they can but they are not the most graceful birds in the air. When they take off, it is low to the water for what seems to be an eternity, its wings flapping like a flag in a stiff breeze and when they land, it's more like a kerplop than a gentle glide. Still, they are exciting to watch as they spear a fish then flip it upward, sometimes several times to get it into a head first in orientation and swallow what is often far more than you would ever bet it could get down.