I disagree with the first answer. Neither is common usage in that you wouldn't say to someone "Oh hello, you have succulent lips" but either would do in a description of someone - say in a book. I think succulent definitely indicated the writer intended you to see the character as attractive and "kissable", whereas fleshy could go either way. They might be attractive lips but they might equally well be fat lips on a fleshy, unsympathetic character.

In english people don't use this. succulent is especially a big word that nobody uses, so don't worry about that word. the only way people describe lips are they say " Big lips or Thick lips or chapped lips"