There is only one Power Flag. Everything else in the power.lib library is a Power Symbol.
There are important differences that you must understand.
A Power Symbol declares a global net whose name is given in the symbol (VCC, VDD, whatever). It has exactly one pin whose type is defined as Power Input. Since it is a Power Input, in order to satisfy ERC the net must be connected to a pin defined as Power Output.
The Power Flag does not declare a net. Its pin is defined as a Power Output. Its purpose is to satisfy the ERC requirement mentioned just above. For example, say your design as an AC input which goes into a rectifier which feeds the input of a voltage regulator. That regulator's VIN pin is likely defined as Power Input, but is a rectifier a "power output?" Strictly speaking, no, and the diodes (and the smoothing cap) have their pins defined as Passive, so ERC will complain: "No driver found for Power Input Pin1 on U1." Placing a Power Flag on the rectifier output net satisfies ERC, because you (as the designer) "know" that the input power for the regulator comes from the AC input though the rectifier.