Choosing the best diet to feed your dog can be a minefield, especially if they are fussy.
As far as raw vs cooked diets go, there is a lot to consider and certain risks and potential benefits everyone needs to be aware of:
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Raw diet risks include - Parasites, Infection (a risk to pet AND owner!), a lack of balance. Raw benefits - nothing proven.
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Cooked commercial diet risks - Contamination, Formulation errors, Faddy/boutique diets are unproven. Benefits - Specific diets proven to be valuable treatment option in certain conditions.
Mixing cooked chicken and other cooked ingredients into a raw diet or cooked commercial diet is absolutely fine, and in fact, cooked chicken (or other meat) has fewer risks than raw meat.
One thing to consider is that adding a significant amount of "extras" to a commercial diet may have the effect of making it unbalanced. If fed as a topper though, to improve the palatability of a diet, this is really unlikely to be a problem.