DOTextSample.cs

using System;
using System.Collections.Generic;
using DG.Tweening;
using UnityEngine;
using UnityEngine.UI;

// see also : http://dotween.demigiant.com/documentation.php
public class DOTextSample : MonoBehaviour
{
    public Text Text;
    public Button Button;
    public List<string> TextList;

    private Tween animationTween;
    private int index = 0;

    void Start()
    {
        if (this.TextList.Count == 0) return;

        this.animationTween = this.CreateAnimationTween(this.TextList[index]);
        this.animationTween.Play();

        this.Button.onClick.AddListener(() =>
        {
            if (this.animationTween.IsPlaying())
            {
                this.animationTween.Complete();
            }
            else if (index < this.TextList.Count)
            {
                this.Text.text = "";
                this.animationTween = this.CreateAnimationTween(this.TextList[index]);
                this.animationTween.Play();
            }
            else
            {
                Debug.Log("completed");
            }
        });
    }

    Tween CreateAnimationTween(string text)
    {
        float duration = this.CalcDuration(text);
        return this.animationTween = this.Text.DOText(text, duration)
            .OnComplete(() => this.index++)
            .SetEase(Ease.Linear);
    }

    float CalcDuration(string text)
    {
        return text.Length * 0.1f;
    }
}