I had a similar issue when adding instruction text boxes to my last project.
How I solved it is by writing the code something to this effect:
func _ready():
visibility = visible
$SlideOne.visible = visibility
$SlideTwo.visible = not visibility
$SlideThree.visible = not visibility
var slide = 1
if Input.is_action_just_released("ui_accept"):
slide = slide + 1
if input.is_action_just_pressed("ui_accept") and slide == 1:
$SlideOne.visible = not visibility
$SlideTwo.visible = visibility
if input.is_action_just_pressed("ui_accept") and slide == 2:
$SlideTwo.visible = not visibility
$SlideThree.visible = visibility
The slide variable indicates which slide, or which bit of dialogue, you're on. So when you push whatever you have for ui_accept, it changes the next slide by making the current one hidden and the next slide visible. It's only when you release the ui_accept button that the slide button is updated, meeting the requirements of the next if statement and letting you progress.
I've noticed, at least in my last project, that some methods either don't move on or skip all the dialogue in one button press. I don't know if this method here will work or even help, but I really hope it does! Good luck!