You can have conflicting conditions that happen at the same time and try to play more than one animation, it is a common problem. You have to add extra conditions to make sure it can't happen, such as adding to your movement controls 'is not jumping' so that it will play the jump animation.
When you are attacking you can set a variable for attack. Then you add to the movement controls and anywhere else it might conflict, 'is not attacking' so that the attack animation plays when you are attacking and the movement plays when you are not attacking.