Try with this change. This way your C# classes will match the JSON object your are receiving. You should of course extend the Data class to include the rest of the json fields if they are of interest to you. 
  public class Response
  {
      [JsonProperty(Required = Required.Default)]
      public string Domain { get; set; }
      [JsonProperty(Required = Required.Always)]
      public Data Data { get; set; }
  }
You will notice that I added the required to AllowNull for Expiration+RegistrantEmail and the Data property to Always. If you send null for Data the deserialization will fail.
  public partial class Data
  {
      [JsonProperty(Required = Required.Default)]
      public bool Available { get; set; }
      [JsonProperty(Required = Required.AllowNull)]
      public object Expiration { get; set; } 
      [JsonProperty("registrant_email" ,Required = Required.AllowNull)]
      public object RegistrantEmail { get; set; }
  }
  var response = JsonConvert.DeserializeObject<Response>(finishResponse);
  Console.WriteLine(response.Data.available);
This answer also considers some of the fields in your serialized json string may be null and thus won't throw exception if that's the case.