Macbook Pro won't start after restart (red charger icon)
It is unlikely that the installation of Flash did anything to your power system, it is likely just a coincidence.

How long have you left the charger plugged in to the Mac? I would give it an hour, minimum, overnight is best.

Failing that try resetting the SMC:

...Press Shift-Control-Option on the left side of the built-in keyboard, then press the power button at the same time. Hold these keys and the power button for 10 seconds.

That is from https://support.apple.com/en-us/HT201295 Their article on resetting the SMC.

If that doesn't work it is possible your battery is dead, time to take it into an Apple store or other Mac repair shop.