環境

Unity5.5
DOTween

コード

test.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

using DG.Tweening;

[RequireComponent(typeof(Camera)),ExecuteInEditMode]
public class FadeEffect : MonoBehaviour {

    private Material material;

    private bool isFade;
    private float _black;

    [SerializeField]
    private float fadeDuration;

    void Awake()
    {
        material = new Material (Shader.Find ("Custom/Fade"));
    }

    void Start()
    {

        StartCoroutine (gameLogic());

    }

    IEnumerator gameLogic()
    {

        yield return FadeOut ();

        Debug.Log ("Done FadeOut");

        yield return FadeIn ();

        Debug.Log ("Done FadeIn");

    }

    public IEnumerator FadeOut()
    {
        isFade = true;

        DOTween.To (black => _black = black, 1.0f, 0.0f, fadeDuration)
            .OnComplete (() => {
                isFade = false;
        });

        yield return new WaitWhile (() => isFade == true);

    }

    public IEnumerator FadeIn()
    {
        isFade = true;

        DOTween.To (black => _black = black, 0.0f, 1.0f, fadeDuration)
            .OnComplete (() => {
                isFade = false;
            });

        yield return new WaitWhile (() => isFade == true);
    }

    void OnRenderImage(RenderTexture source, RenderTexture destination)
    {
        if (isFade) {
            UpdateMaterial ();
            Graphics.Blit (source, destination, material);
        }
    }

    void UpdateMaterial()
    {
        material.SetFloat ("_Black", _black);
    }
}

Fade.shader

Shader "Custom/Fade"
{
	Properties
	{
		_MainTex ("Texture", 2D) = "white" {}
        _Black ("black", float) = 0.0 
	}
	SubShader
	{
		// No culling or depth
		Cull Off ZWrite Off ZTest Always

		Pass
		{
			CGPROGRAM
			#pragma vertex vert
			#pragma fragment frag
			
			#include "UnityCG.cginc"

			struct appdata
			{
				float4 vertex : POSITION;
				float2 uv : TEXCOORD0;
			};

			struct v2f
			{
				float2 uv : TEXCOORD0;
				float4 vertex : SV_POSITION;
			};

			v2f vert (appdata v)
			{
				v2f o;
				o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
				o.uv = v.uv;
				return o;
			}
			
			sampler2D _MainTex;
            float _Black;

			fixed4 frag (v2f i) : SV_Target
			{
				fixed4 col = tex2D(_MainTex, i.uv);
                col = col * _Black;
				return col;
			}
			ENDCG
		}
	}
}

説明

Scriptからmaterialの_BlackをDOTweenで指定時間で1.0/0.0になるように更新。
fragmentシェーダー側でPropertyの_Blackを全ピクセルに加算。

使い方としてはFadeOutの後に何か処理をしてからFadeIn命令を出す感じです。