Funky-sauce is therefore funky music as in James Browns song "It's Too Funky in Here".
A funky sauce that you eat would therfore be sauce containing smoke - i.e. smoke flavouring or an item that was smoked before being made into a sause. i.e. smoked peppers or smoked tomatoes.
But funky can also now mean a strong musty smell of sweat or tobacco. Sauces containing anchovies or fish sauce can therfore be described as being funky as both have a smell similiar to sweat (sweaty socks).
There is a brand of sauce called " Funky Monkey Banana Rum Pepper Sauce" made by Sauce Crafters Ltd of Rivera Beach Florida which contains: Louisiana pepper sauce, bananas, agave nectar, dark rum, apple cider vinegar, habanero peppers, natural sugar, water, chipotle peppers, garlic, xanthan gum.