C# - deserializing JSON in SSIS Script Task

This isn't the C# route, based on my comment and your response you might want to explore doing this in T-SQL. If you haven't before, here is a high level example of how you hook that up in SSIS. As long as you are SQL Server version 2016+

1. Have a variable in SSIS, we'll just call JsonResponse, Type=String
2. You already have your C# Script task to call the web service, add the JsonResponse variable as ReadWriteVariables

3. Modified your script task and write the response to that variable, I'll usually have separate variable the response is streamed to and then assign that to my ReadWriteVariables:

           using (var response = (HttpWebResponse)request.GetResponse())
           {
               using (Stream responseStream = response.GetResponseStream())
               {
                   using (StreamReader streamReader = new StreamReader(responseStream))
                   {
                       responseString = streamReader.ReadToEnd();
                   }
                   Dts.Variables["User::JsonResponse"].Value = responseString;
               }
           }
   

4. After the script task in your Control Flow, add an Execute SQL Task

5. Here you'll have a stored procedure you call that has a @JsonResponse NVARCHAR(MAX) parameter.
6. You'll be passing the above JsonResponse to this stored procedure and with that proc you can then parse that JSON using OPENJSON and do what you will with it. Insert into another table, etc...

Here is an example of what that T-SQL looks like on how you could parse the example you provide. You'd have to obviously make the necessary adjustments to turn that into a stored procedure and adjust accordingly to what you are specifically trying to accomplish:

DECLARE @JsonResponse NVARCHAR(MAX);

SET @JsonResponse = N'
{
    "20": {
        "kpiData": [
            {
                "date": "2018-10-01",
                "interval": "DAILY",
                "kpiFigure": 80,
                "symbol": null,
                "additionalInfo": {}
            },
            {
                "date": "2018-10-02",
                "interval": "DAILY",
                "kpiFigure": 58,
                "symbol": null,
                "additionalInfo": {}
            }
        ],
        "average": 69,
        "weightedAverage": 0,
        "max": 80,
        "min": 58,
        "total": 138,
        "symbol": ""
    },
    "24": {
        "kpiData": [
            {
                "date": "2018-10-01",
                "interval": "DAILY",
                "kpiFigure": 133,
                "symbol": null,
                "additionalInfo": {}
            },
            {
                "date": "2018-10-02",
                "interval": "DAILY",
                "kpiFigure": 130,
                "symbol": null,
                "additionalInfo": {}
            }
        ],
        "average": 132,
        "weightedAverage": 0,
        "max": 133,
        "min": 130,
        "total": 263,
        "symbol": ""
    }
}
';

SELECT [a].[Key] AS [SiteID]
     , [b].*
FROM   OPENJSON(@JsonResponse) [a]
CROSS APPLY OPENJSON([a].[Value], '$.kpiData')
           WITH (
                    [date] DATE '$.date'
                  , [interval] NVARCHAR(100) '$.interval'
                  , [kpiFigure] INT '$.kpiFigure'
                ) [b];

Just an option/example of how you can get that JSON over to T-SQL and parse it from there.