Chicken didn't retain flavour from marinade
The scientific foundation for this answer is in the fantastic post pointed out in the comments here.


How can I better ensure that the flavour seeps into the meat more
uniformly?


Basically there are two parts to this problem, as pointed out by the other post - one part is the composition of your flavor components that you want to penetrate the meat, and as discussed at length in the original post, more lipossoluble molecules and smaller molecules penetrate the meat better; the other one is the surface area to volume ratio of your chicken, for the molecules that will have more difficulty in reaching the deep confines of the chicken, so in that case, the smaller pieces of chicken you use, the better. 

This is essentially the scientific foundation for why wings and legs are more flavorful than breast, especially when it is a whole chicken. 


How do I prevent "spotty" flavouring in the future?


Either change the composition of your marinade (this one is very water soluble and has a lot of big flavor molecules) or cut your chicken in smaller pieces (so the surface area to volume ratio is better).

If you want to change the composition of your marinade to include more oil-soluble substances, I advise you to use buttermilk as a liquid, since it has a larger oil-to-water ratio and it will be a better solvent for your additional spices and ingredients. For a suggestion on the ingredients, the chili family in general contains capsaicin which is liposoluble and gives the spicy kick; black pepper, anise, cloves and nutmeg all contain eugenol, which is a small molecule and also has a good solubility in fat and gives the aromatic aspect; you can also use roasted sesame oil for the smokey depth and an Asian-like feel. 


Would poking the chicken, just to break the skin, have helped?


If it is just breaking the skin, not really. What really helps is injecting, so you get more surface for your brine to permeate the chicken.