What should you do with wood chips left after tree stump grinding?

Before you move that pile to your flower beds, leave a good amount of it right over the hole where the stump used to be. Rake it into a mound that sits a bit higher than the rest of the yard. The old roots left underground are going to rot over the next year or two, and that spot will sink. If you make it perfectly level today, you will end up with a crater later.

Take whatever is left over and use it in your flower beds. The nitrogen issue you mentioned is a very common worry, but it only happens if you actually mix or till the wood chips down into the soil. If you just spread the mix on top of the dirt as a mulch, it will not rob nitrogen from your plants.

Since you are dealing with the heat in Sharjah, putting a two or three-inch layer of this over your beds is highly recommended. It shades the soil and stops your irrigation water from evaporating so fast. Because stump grindings are a messy mix of shredded wood and dirt rather than pure bark, it will break down faster than bagged mulch. This is actually great for adding organic matter to the soil as it decomposes.
Just keep the mulch pulled a few inches away from the actual stems of your flowers and the trunks of any other trees. If wet wood sits directly against a plant stem, it causes rot. Spread it around the plants rather than piling it against them, and do not try to plant new flowers directly into the wood chips themselves.