Catching pokemon, transfering, hatching egg all brings candies. Are there other ways to increase the candy amount?
For example if I use my lucky egg, would I be able get 2x candies from transferring?
The ways you currently described are currently the only way to get more candy.
Also a lucky egg doubles your exp gain for 30 minutes, it does nothing else.
There are currently no other known ways to obtain candies besides the ones you just mentioned.
To improve your candy rates you can however use lures. As this will increase the amount of pokémon encountered, indirectly boosting your candy income.