University of Chicago Celiac Disease Program has suggested guidelines for those interested in reintroducing oats into the diet. Unfortunately, I wasn't able to find it on their website so I'll update this post after I receive their response.
I found two companies that provide gluten-free oats, but it occurs to me that there may be more.
The first is from Montana grown Gluten Free Oats . According to the website the oats are "SAFE for people who are gluten intolerant because they are tested to be below 10 parts per million (ppm) by the University of Nebraska FARRP Laboratory." A 1.25 pound box of Gluten Free Oats cost $5.75. A 25 pound box costs $87.75. They offer other sizes as well.
The other company I found that offers gluten-free oats is Cream Hill Estates. Cream Hill Estates "oats consistently test below or near the test's[Elisa test] lower limit of detection, which is two (2) parts per million." A 1kg box which is nearly 2 pounds costs $8.99 when ordered from The Gluten Free Pantry.
For those who are not yet ready to try oats, quinoa flakes make a good substitute in baked goods.