The current code use OnGraphStop() to restore flip state but OnGraphStop() will also be called when Timeline is just paused. The follow is a fix. It use 'stopped' event from playableDirector so that even pausing the timeline won't revert the flip state.

using System;
using UnityEngine;
using UnityEngine.Playables;
using UnityEngine.Timeline;

using Spine.Unity;

namespace Spine.Unity.Playables {
   public class SpineSkeletonFlipMixerBehaviour : PlayableBehaviour {
      float originalScaleX, originalScaleY;
      float baseScaleX, baseScaleY;

  SpinePlayableHandleBase playableHandle;
  bool m_FirstFrameHappened;

    public override void ProcessFrame (Playable playable, FrameData info, object playerData) {
     playableHandle = playerData as SpinePlayableHandleBase;

     if (playableHandle == null)
        return;

     var skeleton = playableHandle.Skeleton;

     if (!m_FirstFrameHappened) {
        originalScaleX = skeleton.ScaleX;
        originalScaleY = skeleton.ScaleY;
        baseScaleX = Mathf.Abs(originalScaleX);
        baseScaleY = Mathf.Abs(originalScaleY);
        m_FirstFrameHappened = true;
     }

     int inputCount = playable.GetInputCount();

     float totalWeight = 0f;
     float greatestWeight = 0f;
     int currentInputs = 0;

     for (int i = 0; i < inputCount; i++) {
        float inputWeight = playable.GetInputWeight(i);
        ScriptPlayable<SpineSkeletonFlipBehaviour> inputPlayable = (ScriptPlayable<SpineSkeletonFlipBehaviour>)playable.GetInput(i);
        SpineSkeletonFlipBehaviour input = inputPlayable.GetBehaviour();

        totalWeight += inputWeight;

        if (inputWeight > greatestWeight) {
           SetSkeletonScaleFromFlip(skeleton, input.flipX, input.flipY);
           greatestWeight = inputWeight;
        }

        if (!Mathf.Approximately(inputWeight, 0f))
           currentInputs++;
     }

     if (currentInputs != 1 && 1f - totalWeight > greatestWeight) {
        skeleton.ScaleX = originalScaleX;
        skeleton.ScaleY = originalScaleY;
     }
  }

  public void SetSkeletonScaleFromFlip (Skeleton skeleton, bool flipX, bool flipY) {
     skeleton.ScaleX = flipX ? -baseScaleX : baseScaleX;
     skeleton.ScaleY = flipY ? -baseScaleY : baseScaleY;
  }

  // NOTE: Cannot use this because Pause will also trigger.
  /* 
    public override void OnGraphStop(Playable playable)
    {
        m_FirstFrameHappened = false;

        if (playableHandle == null)
            return;

        var skeleton = playableHandle.Skeleton;
        skeleton.ScaleX = originalScaleX;
        skeleton.ScaleY = originalScaleY;
    }
  //*/

  // NOTE: instead, subscribe to stopped event 

  PlayableDirector director = null;

  public override void OnPlayableCreate(Playable playable)
  {
     director = playable.GetGraph().GetResolver() as PlayableDirector;
     director.stopped += OnTimelineStopped;
  }

  public override void OnPlayableDestroy(Playable playable)
  {
     director.stopped -= OnTimelineStopped;

     base.OnPlayableDestroy(playable);
  }


  void OnTimelineStopped(PlayableDirector obj)
  {
     m_FirstFrameHappened = false;

     if (playableHandle != null)
     {
        var skeleton = playableHandle.Skeleton;
        skeleton.ScaleX = originalScaleX;
        skeleton.ScaleY = originalScaleY;
     }
  }

   }

}