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Okay guys this is killing me,

In my makefile, I tell it to use G++ along with some custom flags to compile, but those flags do not appear to work, they don't even appear in a command line.

Makefile:
CPP_FILES := $(wildcard source/*.cpp)
OBJ_FILES := $(patsubst %.cpp,%.o,$(CPP_FILES))
LD_FLAGS := -T linker.ld
CC_FLAGS := -ggdb -Wall -Wextra -nostdlib -fno-builtin -nostartfiles -nodefaultlibs -fno-exceptions -fno-rtti -fno-stack-protector -fleading-underscore

kernel.bin: $(OBJ_FILES) ; ld $(LD_FLAGS) -o kernel.bin boot.o $(OBJ_FILES)

source/%.o: source/%cpp ; g++ $(CC_FLAGS) -o $@ $<

P.S: LD_FLAGS work flawlessly

Do you mean source/%.cpp?
if things does not match any rule, the default action would be made such as invoke g++ without your custom flags.

The easiest way is to replace or insert echo checkpoints to debug, which is essential skill for general programming.

What's the semicolon doing there?

Everything after the colon is the dependency. The command(s) to be executed should be on subsequent lines, starting with a tab. This is important!
You might want to check out the Makefile tutorial for more things regarding 'make'.

Yeah thanks that worked, but how do I go on adding ASM code support, because this doesn't work

PROJECT_DIRS := source
CPP_FILES := $(wildcard source/*.cpp)
ASM_FILES :=$(wildcard source/*.asm)
OBJ_FILES := $(patsubst %.cpp,%.o,$(CPP_FILES))
ASM_OBJ :=$(patsubst %.asm,%.o,$(ASM_FILES))
LD_FLAGS := -T linker.ld
CC_FLAGS := -ggdb -Wall -Wextra -nostdlib -fno-builtin -nostartfiles -nodefaultlibs -fno-exceptions -fno-rtti -fno-stack-protector -fleading-underscore

kernel.bin: $(OBJ_FILES)
ld $(LD_FLAGS) -o kernel.bin $(OBJ_FILES) $(ASM_OBJ)

source/%.o: source/%.cpp
g++ $(CC_FLAGS) -o $@ $<
source/%.o: source/%.asm
nasm -f elf -o $@ $<

As a positive suggestion you should read Getting_Started, specifically Required Knowledge & Toolchain

To your question, it's quite obvious you didn't include assembly files in your definition of OBJ_FILES; or otherwise include ASM_OBJ in kernel.bin.

Gotcha,

Well sorry guys, I had my OS compiling but the problem was that it was a bash file and everytime I added a file, I needed to make changes myself, so I looked into makefile, even though with some fail

Make sure you really understand 'make'. Using a half-understood tool in a non-trivial project is an error source unto itself.

For example, your Makefile doesn't cater to changes made in header files. You change a constant in a header file, you might be in for a lengthy debug session before you realize that your object files didn't get recompiled. Might I recommend the Makefile tutorial a second time?