Simple way to detect swipes in unity. Reference the monobehaviour and you're done.

SwipeGestures.cs

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

public enum SwipeGesture { SwipeUp, SwipeDown, SwipeLeft, SwipeRight, None };

/// <summary>
/// Simplest usage:
///
/// public SwipeGestures Gestures; // Reference to MonoBehaviour
///
/// if(Gestures.ThisFrame == SwipeGesture.SwipeUp)
///   DoSomething();
///
/// </summary>

public class SwipeGestures : MonoBehaviour {

   /// <summary>
   /// E.G: Min Delta of .2 is 20% of screen
   /// This is normalized towards the bigger screen that way you need
   /// to move the same amount of pixels for non-square screens
   /// </summary>
   
   [SerializeField]
   private float _minDelta = .2f;

   /// <summary>
   /// Set to true if you want to use mouse in addition to touch coords
   /// </summary>
   public bool UseMouse = true;
   private const int mouseHash = 123456;

   private SwipeGesture _swipeGestureThisFrame = SwipeGesture.None;
   private int _lastFrameUpdated = 0;
   /// <summary>
   /// Returns the swipe gesture this frame
   /// </summary>
   public SwipeGesture ThisFrame {
      //use lazy loading to ensure the input location has been updated
      get {
         EnsureInputsAreFactoredIn();
         return _swipeGestureThisFrame;
      }
   }

   /// <summary>
   /// Gets called on swipe gesture
   /// </summary>
   public event Action<SwipeGesture> OnSwipeGesture;

   private Vector2 minDeltaPixels {
      //normalized means its a swipe after N pixels, regardless of if its
      //x or y
      get {
         float w = Screen.width * _minDelta;
         float h = Screen.height * _minDelta;
         if (w > h)
            w = h;
         else
            h = w;
         return new Vector2(_minDelta * w, _minDelta * h);
      }
   }

   Dictionary<int, Vector2> _inputStartPositions;

   void Awake() {
      OnSwipeGesture = (a) => { };
      _inputStartPositions = new Dictionary<int, Vector2>();
      _swipeGestureThisFrame = SwipeGesture.None;
   }

   //Call this at least once a frame otherwise
   // it will miss start positions
   void EnsureInputsAreFactoredIn() {
      if (_lastFrameUpdated < Time.frameCount) {

         SaveStartPositions();

         if (Input.mousePresent &&
            UseMouse &&
            _inputStartPositions.ContainsKey(mouseHash)) {

            var startPos = _inputStartPositions[mouseHash];
            var delta = ((Vector2)Input.mousePosition) - startPos;
            if (AccountForDelta(delta))
               _inputStartPositions.Remove(mouseHash);
         }

         if (Input.touchSupported) {
            foreach (var touch in Input.touches) {
               if (_inputStartPositions.ContainsKey(touch.GetHashCode())) {
                  var startPos = _inputStartPositions[touch.GetHashCode()];
                  var delta = touch.position - startPos;
                  if (AccountForDelta(delta))
                     _inputStartPositions.Remove(touch.GetHashCode());
               }
            }
         }
      }
      _lastFrameUpdated = Time.frameCount;
   }

   void Update() {
      EnsureInputsAreFactoredIn();
   }

   // return true if accounted for delta
   // this function sets all the variables for each delta
   private bool AccountForDelta(Vector2 delta) {
      if (delta.x > minDeltaPixels.x) {
         _swipeGestureThisFrame = SwipeGesture.SwipeRight;
         OnSwipeGesture(SwipeGesture.SwipeRight);
         return true;
      }

      if (delta.x < -minDeltaPixels.x) {
         _swipeGestureThisFrame = SwipeGesture.SwipeLeft;
         OnSwipeGesture(SwipeGesture.SwipeLeft);
         return true;
      }

      if (delta.y < -minDeltaPixels.y) {
         _swipeGestureThisFrame = SwipeGesture.SwipeDown;
         OnSwipeGesture(SwipeGesture.SwipeDown);
         return true;
      }

      if (delta.y > minDeltaPixels.y) {
         _swipeGestureThisFrame = SwipeGesture.SwipeUp;
         OnSwipeGesture(SwipeGesture.SwipeUp);
         return true;
      }

      return false;
   }


   //this function makes sure the start positions are in the dictionary
   //You must call it every frame in case new touches are added
   private void SaveStartPositions() {
      foreach (var touch in Input.touches) {
         var h = touch.GetHashCode();
         if (touch.phase == TouchPhase.Began)
            _inputStartPositions.Add(h, touch.position);
         if (touch.phase == TouchPhase.Ended || touch.phase == TouchPhase.Canceled)
            _inputStartPositions.Remove(h);
      }

      if (Input.GetMouseButtonDown(0)) {
         _inputStartPositions.Add(mouseHash, Input.mousePosition);
      }
      if (Input.GetMouseButtonUp(0)) {
         _inputStartPositions.Remove(mouseHash);
      }
   }
}