How to make character fly?

Hello. I am new in Unity and since few day I try to figure out how to make my third person character fly correctly.
I want my character fly while some key push and when release it fall but can move left and right while fall.
If I use Character Controller translate.Transform ignore physics object and if I use Move() its just jump. Character Controller automatic add gravity only to my animator not to cube;
If I use Rigidbody the animator fail on his face when walk if use kinimatic if go throw object.
the project is 3D but move only on X,Y axis.

Link to character assets:https://assetstore.unity.com/packages/3d/animations/warrior-pack-bundle-2-free-42454

What is the best way to make third person character simple fly?