Is it possible that training after a lymphatic drainage massage, spread toxins around the body and cause flu like symptoms?

Not usually: For those with compromise of lymphatic drainage, manual lymphatic drainage moves the lymph fluid around the blocked area and gets it to where it needs to go. The movement of the lymph fluid which may contain bacteria, fungus, viruses or very digested food goes finally to the big blood vessels to be sent to processing areas. Training probably does not add much movement to already moving lymph.