What is the battery recommendation if need to use battery to power up BL654PA?

Answer

The power input in data sheet is 3.0v~5.5v, and at least need to have 2.8v to make the internal LDO work.

Li-ion, Li-poly nominal battery voltage is 3.6V fully charged, and are recommended to power BL654PA.  3*AAA battery is also recommended as well.