Dragon ferocity gives 1/2 str to damage in addition to the normal str to damage. But this FAQ* tells us that you can not add the same ability twice. So unless you have str to damage it seems dragon style now does not add damage.
No. An ability bonus, such as "Strength bonus", is considered to be the same source for the purpose of bonuses from the same source not stacking. However, you can still add, for instance “a deflection bonus equal to your Charisma modifier” and your Charisma modifier. For this purpose, however, the paladin's untyped "bonus equal to her Charisma bonus (if any) on all saving throws" from divine grace is considered to be the same as "Charisma bonus (if any)", and the same would be true for any other untyped "bonus equal to her [ability score] bonus" constructions.
Edit: I would not play it that way. But, as I read it, that is the RAW because of the FAQ.
Dragonstyle doesn't add 1/2 str to damage. It's worded, same as power attack, to add 1.5 your str to damage. As it's multiplied before adding it that FAQ doesn't apply.
Dragon ferocity will be errata'd so that it works.
(EDIT: was a little confused as you refer to Ferocity in your title and Style in the body of your post, so addressed both)
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