So, I just installed the flat assembler for windows (win 10 64 bit). And I tried to run this program:
format PE

int3
mov eax,1
mov ebx,2
mov ecx,16

The int3 instruction should call the debugger out of the box, or do I need to do something?

You need to register your debugger with the OS to handle the events.

For example, Ollydbg gives you a menu option to enable the capture of int3 and some other events.

This is also known as JIT debugging.