Can I use Vreg output to power AD805 current sense amplifier? Is there apower restriction?
You can use Vreg to power up AD805. This device uses only 2 mA current (max). Linear (now Analog Devices) use Vreg to power EEPROM in demoboard for LTC6811 which  has also only mA current consumption.

PS. But your schematic is wrong. You must use NPN transistor to Vreg as shown in datasheet.