You are in an enviable situation!! Wood chips make the best mulch, then break down to make great compost. You seem to have a bit of both! Your flowers will thank you! With this drought we are experiencing here in Pa I have been going daily to my wood chip pile left by the phone company after removing a lot of trees two years ago and trying to save my flower gardens. You can add the wood chips themselves to the soil. As long as you don't mix it in to the soil already there it will just break down naturally and not deplete the nitrogen in your soil. The compost part should be pretty well balanced by this time. No matter what it is a win win situation for you!
I have augmented the chips by adding some rabbit manure to the soil, watering and then putting the chips on top of that.
I have a chipper/shredder and add wood chips to my compost piles quite often with good results.
This photo shows the piles of chipped/shredded materials in the front while the darker piles in back are the finished product.