74HC14 VCC and GND won't connect even with PWR_FLAGs attached to board input connector

I suspect you follow an outdated tutorial. The current version of the library luckily has gotten rid of the hidden power pins for the 74xx library (sadly some other logic libs still have them, we simply did not have the manpower during the v5 development phase).

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This means the power pins are on a separate unit (for all of them the last unit is the one with the power pins). You need to place that unit and connect the pins like any other pin.

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There are good reasons for not allowing symbols with hidden power pins. The main ones are that such symbols are very restrictive as they do not allow for having more than one power supply, and they are unsuited for an environment with strict documentation guidelines. There is not much of a downside so the decision was quite easy to make.

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Plus you misunderstand the purpose of the PWR_FLAG symbol. This symobl has no influence on what gets connected to what! It is just a symbol with a single power output pin. That is needed as KiCads ERC ensures that every power input pin is connected to a power output pin (every net with a power input pin must have a power output connected). However, as most designs use generic connectors for the power supply you will need to tell ERC where the supply comes from. So one option is to connect the PWR_FLAG symbol as it then provides the power output for the net it is connected to.