While people do use both garlic and Vitamin C for 'health' benefits for the pets; it should be noted that garlic is technically toxic to dogs and excess vitamin C can help increase the risk for bladder stones. Garlic, and any member of the Allium genus has a n-propyl disulfide compenent that appears to have oxidative toxic effects to the pet's red blood cells (RBC's).
As far as holistic methods to reduce Kennel Cough. The vaccination is designed to help stop the bacteria Bordetella bronchiseptica. It is only one of over a dozen different agents that cause URI - Upper Respiratory Infections or ITB Infectious TracheoBronchitis (depending upon which term you like).
Thus I think that focusing on maintaining a healthy immune system along with avoiding high risk areas of ITB is a great idea whether you vaccinate or not. One note on vaccination - the intranasal version lasts a year and is relatively low on side effects.
Some people have reported immune system health with the use of probiotics, Missing Link supplement, royal jelly and echinacea. Aside from the probiotics, I cannot say how well the other ones work but I have not heard of toxicity issues/etc...
The use of antioxidants and Omega 3 fatty acids also have a positive effect on the immune system.
Regular exercise and maintaining proper body weight also helps promote a healthy immune system.
I bet some of the members here could comment on dietary options that might help support the immune system.
Hope it helps.