My macbook pro battery charging is flickering between on and off - how do I fix this?

Try an SMC Reset.

Try unplugging the charger from the electrical outlet for a minute to reset the charger's internal circuitry.

Check the magsafe port on the laptop to make sure there are no staples or other metal bits stuck to the magnet preventing the charger from seating properly.

Check the condition of the battery by Option-clicking the battery icon on the menubar. A good battery will show as "Normal" or "Good", but if the condition is "Service Battery", then macOS has detected an internal hardware fault with the battery so the battery will need to be replaced.

Run the Apple Diagnostics to see if any hardware issues are detected.

Here is an Apple article for troubleshooting Magsafe charging issues:

https://support.apple.com/en-us/HT203207

If these steps do not help, then you will need to have Apple or an Apple Authorized Service Provider examine the laptop and provide you with an estimate for the repair.