I know that outside of battle, using Softboiled can heal another pokemon's HP. But how much does it take from the user (e.g. Chansey) and give to the other pokemon?
20% of Chansey/Blissey HP. This fails if HP is below 20%. This can be used as many times that you want until then.
Outside of battle, Softboiled can be used to heal other Pokémon that you are carrying. The Pokémon using Softboiled removes up to 20% of its own HP and restores them to the wounded Pokémon. Same thing for the move milk drink. (it can be used out of battle too) The move won't always work though. say I have a chansey. If it's health is more than 80% gone, then the move won't work out of battle. It'll also fail if the pokemon you're trying to heal is at full health.