Dan's stones will be pretty flat, but what you need is one of these. In fact this one is mine and was purchased from Dan's several years ago.
As the owner of a lapping machine purchased from them, I would say I am a bit of an expert on the subject, and its my opinion that the machine will get it VERY flat, but I do like to lap them on 600 to 2000 grit wet dry paper on a marble tile, I have found that the machine does 99% of the work but I do prefer to get that last 1% out by hand.
One other trick I have used before and had great luck with is to use some diamond paste and rub two of the stones together, or on the marble slab or such, no real proof it does anything, but I really like the glossy look after.
I recorded this video the other day, the machine has been sitting under moth balls for about 4 years, taking up space in my garage, I have a guy I am probably going to sell it to, (and sending it back to Arkansas where it belongs) but before I sell it I thought I would get a few hundred stones lapped out before I do.
that and HAD got to me recently which is fun. :)
https://www.youtube.com/watch?v=lbW3OlWa2vs