The first task is to sand back any flaking paint. I personally use a Ryobi 18V ONE+ Random Orbital Sander and highly recommend it as it is a great option that copes well with large jobs and intricate work. I also own a belt sander and larger random orbital but this unit is by far the most used.
I would suggest starting with an 80 grit pad and knocking off all the larger flaking paint. Don't press too hard as you'll leave scratches in the timber. Once the bulk of the paint is removed you should step up to a 120 grit and start working down to bare timber.
Once all the old paint is removed you can then coat with new paint. If you want to oil the timber and keep the natural look there is more work to do. You'll notice that there is still paint between the slats which you won't be able to remove without a lot of elbow grease. The only way I can think of to remove that paint is by sliding a piece of sandpaper between the slats and working it back and forth.