What's the best way to pour post footings under a patio slab?
Your question seems to be simply whether you can bell out the hole for the footing. Yes, you can. Footing specifications are for the footing structure itself, not where or how you access the space occupied by the footing. The opening in the patio would only need to be large enough for concrete to pass through, but obviously you'll need to get a post-hole digger or other tool in there as well.
You might get better answers and suggestions if updated your question post with some information about your project. Narrowly-scoped questions like this aren't terribly helpful to you or the community.