I need some help understanding where this error is occurring:
warning: in-class initialization of non-static data member is a C++11 extension [-Wc++11-extensions]
This is the section of the code that it is coming from:
typedef struct Hand {
bool straight = false;
bool flush = false;
bool four = false;
bool three = false;
int pairs = 0;
} Hand;
That's not an error, it's a warning. It tells you that you're only allowed to initialize non-static members of a struct / class starting with the C++11 standard (so called because it was published in 2011). Before that, you weren't officially allowed to by C++98 (published, you've guessed it, in 1998). Long story short, what you're doing has only become legal, official C++ in 2011. Your compiler's default seems to be the 1998 standard.
Try compiling with -std=c++11
as a command line flag (assuming you're using GCC or clang), and the warning should go away. If you're using a different compiler, there should be a flag for that as well (if it's recent enough to implement C++11).