I have a gaming chair who's charger requires 12V/10A, is it possible to take a wire with the right plugin, and combine it with a completely different cord whose power box has the right voltage/amprage??
Yup.
You need to match voltage amount and type. DC-DC or AC-AC... never mix and match.
Polarity is important too... make sue when you attach the replacement that the + and - are not accidentally swapped.
Current is a little more forgiving. 10A is the minimum required, you are allowed to provide more than this.
Current rating on a supply is how much it can supply up to.
Current rating on a device is how much it will pull. If you use a 20A supply, your charger will only pull 10A of that.
Voltage must always be matched exactly though!