Proof of concept. Put in Editor folder and toggle in menu (Tools/Toggle XZ flight).

SceneViewXZFlight.cs

using UnityEditor;
using UnityEngine;

[InitializeOnLoad]
public static class SceneViewXZFlight
{
	private static readonly float SlowSpeed = 0.5f;
	private static readonly float FastSpeed = 2.0f;

	private static bool movingCamera = false;
	private static Vector3 v = Vector3.zero;

	private static bool Enabled {
		get => EditorPrefs.GetBool("SceneViewXZFlight", false);
		set => EditorPrefs.SetBool("SceneViewXZFlight", value);
	}

	static SceneViewXZFlight()
	{
		SceneView.duringSceneGui -= OnSceneGUI;
		SceneView.duringSceneGui += OnSceneGUI;
	}

	[MenuItem("Tools/Toggle XZ flight")]
	public static void Toggle()
	{
		Enabled = !Enabled;
	}

	private static void OnSceneGUI(SceneView sceneView)
	{
		if (!Enabled) return;

		Event e = Event.current;
		switch (e.type)
		{
		case EventType.MouseDown:
			OnMouseDown(e);
			break;
		case EventType.MouseUp:
			OnMouseUp(e);
			break;
		case EventType.KeyDown:
			OnKeyDown(e);
			break;
		case EventType.KeyUp:
			OnKeyUp(e);
			break;
		case EventType.Repaint:
			OnRepaint(sceneView, e);
			break;
		case EventType.MouseLeaveWindow:
			OnMouseLeave(e);
			break;
		case EventType.MouseDrag:
			OnMouseDrag(sceneView, e);
			break;
		}
	}

	private static void OnMouseDown(Event e)
	{
		if (e.button == 1)
		{
			movingCamera = true;
			v = Vector3.zero;
			e.Use();
		}
	}

	private static void OnKeyDown(Event e)
	{
		switch (e.keyCode)
		{
		case KeyCode.W:
			v.z = 1.0f;
			break;
		case KeyCode.S:
			v.z = -1.0f;
			break;
		case KeyCode.A:
			v.x = -1.0f;
			break;
		case KeyCode.D:
			v.x = 1.0f;
			break;
		case KeyCode.Q:
			v.y = -1.0f;
			break;
		case KeyCode.E:
			v.y = 1.0f;
			break;
		}
	}

	private static void OnKeyUp(Event e)
	{
		switch (e.keyCode)
		{
		case KeyCode.W:
		case KeyCode.S:
			v.z = .0f;
			break;
		case KeyCode.A:
		case KeyCode.D:
			v.x = 0.0f;
			break;
		case KeyCode.Q:
		case KeyCode.E:
			v.y = 0.0f;
			break;
		}
	}

	private static void OnMouseDrag(SceneView sceneView, Event e)
	{
		if (!movingCamera) return;

		Camera c = sceneView.camera;
		Transform t = c.transform;
		Vector3 pivot = sceneView.pivot;
		Vector3 cameraPosition = t.position;
		Vector3 cameraToPivot = pivot - cameraPosition;
		Vector3 cameraRight = t.right;
		Vector2 mouseD = e.delta;

		Quaternion qy = Quaternion.Euler(0.0f, mouseD.x * Time.deltaTime, 0.0f);
		Quaternion qx = Quaternion.AngleAxis(mouseD.y * Time.deltaTime, cameraRight);
		Quaternion q = qx * qy;
		cameraToPivot = q * cameraToPivot;
		Quaternion rotationToPivot = Quaternion.LookRotation(cameraToPivot);
		pivot = cameraPosition + cameraToPivot;

		sceneView.pivot = pivot;
		sceneView.rotation = rotationToPivot;

		sceneView.Repaint();
	}

	private static void OnRepaint(SceneView sceneView, Event e)
	{
		if (!movingCamera) return;

		Camera c = sceneView.camera;
		Transform t = c.transform;
		Vector3 cameraRight = t.right;
		Vector3 pivot = sceneView.pivot;

		Vector3 forward = new Vector3(-cameraRight.z, 0.0f, cameraRight.x);
		Quaternion q = Quaternion.LookRotation(forward);

		float speed = e.shift ? FastSpeed : SlowSpeed;
		
		pivot += (q * v) * speed * Time.deltaTime;

		sceneView.pivot = pivot;
		sceneView.Repaint();
	}

	private static void OnMouseUp(Event e)
	{
		if (e.button == 1)
		{
			movingCamera = false;
			e.Use();
		}
	}

	private static void OnMouseLeave(Event e)
	{
		movingCamera = false;
		e.Use();
	}
}