counting consecutive null characters

[Lindley]

That looks a bit over complicated. How about...

#include <string>
#include <algorithm>

int checkConNullBytes(const std::string &dataStream)
{
    int maxCount = 0;
    int count = 0;

    std::string::const_iterator begin = dataStream.begin();
    std::string::const_iterator end = dataStream.end();

    while (begin != end)
    {
        if (*begin == 0)
        {
            ++count;
            maxCount = std::max(maxCount, count);
        }
        else
        {
            count = 0;
        }
    
        ++begin;
    }

    return maxCount;
}

int main()
{
    char data[] = {0, 1, 2, 3, 0, 0, 4 ,5 ,0, 0, 0, 6, 7};

    std::string dataStream(data, data + 13);

    int largest = checkConNullBytes(dataStream);
}

If you expect the string to have mostly 0s, you should put the std::max call in the else rather than the if (prior to resetting count). If you expect the 0s to be fairly rare, it'll be faster as-is.