You can just add a bit of recursivity to your code, something like this:

var set = new DataSet();
AddToDataSet(set, resp);

...

public static void AddToDataSet(DataSet set, object value)
{
    if (set == null)
        throw new ArgumentNullException(nameof(set));

    if (value == null)
        return;

    var type = value.GetType();
    var table = set.Tables[type.FullName];
    if (table == null)
    {
        // create one table per type (name)
        table = new DataTable(type.FullName);
        set.Tables.Add(table);
        foreach (var prop in type.GetProperties().Where(p => p.CanRead))
        {
            if (IsEnumerable(prop))
                continue;

            var col = new DataColumn(prop.Name, prop.PropertyType);
            table.Columns.Add(col);
        }
    }

    var row = table.NewRow();
    foreach (var prop in type.GetProperties().Where(p => p.CanRead))
    {
        object propValue = prop.GetValue(value);
        if (IsEnumerable(prop))
        {
            if (propValue != null)
            {
                foreach (var child in (ICollection)propValue)
                {
                    AddToDataSet(set, child);
                }
            }
            continue;
        }

        row[prop.Name] = propValue;
    }
    table.Rows.Add(row);
}

private static bool IsEnumerable(PropertyInfo pi)
{
    // note: we could also use IEnumerable (but string, arrays are IEnumerable...)
    return typeof(ICollection).IsAssignableFrom(pi.PropertyType);
}