Hard to say without seeing your animation code, but generally you would only set a jumping or falling animation when
is_on_floor() is false. The logic would be something like:
if velocity.y > 0:
The character sliding down the slope on his own is a little more advanced since you would have to make use of the moveandslidewithsnap() function. This keeps the character "snapped" to the floor even when gravity is being applied. Just note that you would also have to "unsnap" the player when jumping. For a tutorial, check out this Pigdev video.