That is a very old version of flint. It is better to build the latest version yourself from source.
Below I will assume your home directory is /home/malay. If not, you will have to change that path below. You may also like to use make -j instead of just make if you have multiple cores.
tar -xvf mpir-2.7.0-alpha4.tar.bz2
tar -xvf mpfr-3.1.2.tar.bz2
tar -xvf flint-2.4.3.tar.gz
cd mpir-2.7.0
./configure --enable-gmpcompat
make
cd ..
cd mpfr-3.1.2
./configure --with-gmp-build=/home/malay/mpir-2.7.0
make
cd ..
cd flint-2.4.3
./configure --with-mpir=/home/malay/mpir-2.7.0 --with-mpfr=/home/malay/mpfr-3.1.2
make
cd ..
Anyway, to answer your original question, you are missing
-I/home/malay/mpir-2.7.0 -I/home/malay/flint-2.4.3
when running gcc above. It can't find flint.h, fmpz_poly.h or fmpz_mod_poly.h because you didn't tell it where to look. That's what the -I does. (that's I for include by the way, not the letter l).
You will also need to tell it where to find the libraries by passing
-L/home/malay/mpir-2.7.0/.libs -L/home/malay/mpfr-3.1.2/src/.libs -L/home/malay/flint-2.4.3
to gcc.
You should also have
#include "flint.h"
#include "fmpz_poly.h"
#include "fmpz_mod_poly.h"
i.e. using double quotes, not angle brackets, since they are not standard library headers.
Bill.