If you installed or updated K9 / Kaiten (K10) mail after installing our application, you will need to re-install our application due to how permissions work in Android.
Another issue may be that your accounts do not have a name in K9 or Kaiten mail. In order for them to show up in our apps, you have to assign them a name.
Additionally, if your K9/K10 mail installation is brand new, please make sure that you allow about an hour for everything to sync up before adding your account to our app.
After doing this, you should be able to see accounts listed on your device!