What we found...
The research varies based on the sample size and sample age
There was no effect of gender or diet on any of the immune parameters measured. After the 10-month exercise-training period, significant differences in antibody response between the exercise and control groups were observed. The exercise group had a greater mean fold increase in antibody titer than the control group in response to influenza. The results suggest that although exercise may enhance antibody production in response to vaccination in adults, exercise does not eliminate age-associated changes in immune function. Exercise is often recommended for adults, however, there are not many studies demonstrating that REGULAR exercise can improve immune response to a viral antigen. (pg. 2298)
Also, we have found with the research that it goes both ways. Some research found that it does improve immune response of the flu vaccine and other state it does not
Influenza is known to cause severe respiratory tract infections each year. Several studies have even looked at exercise as another form of an influenza vaccine adjuvant examined from aerobic and anaerobic types of exercise.
Women in the exercise had a significant amount of antibody titers against H1N1 influenza strain than men. Acute moderate aerobic exercise was not immune-stimulatory in healthy older men.