You cant train reflexes, theyre automatically programmed into your genes lol. But you can sensitize and desensitize yourself (classical conditioning also). Essentially, your body will always go into fight or flight (your sympathetic nervous system), but you can act on that impulse sooner with conditioning
You do have to kinda hack your own instincts. For me, when i get anxious (fight or flight) i try to do things that an organism would do if a predator/threat wasnt present (eating (slowly), breathing calmly, etc). The body kinda figures (well if were doing this, the threats probably passed). This method is good for anxiety about things that arent real bodily threats