The Dogmatika engine itself is pretty consistent, relying on Dogmatika Ecclesia, the Virtuous as the main search, with Dogmatika Adin, the Enlightened as a backup normal summon for this engine. Dogmatika Fleurdelis, the Knighted essentially provides a hand trap (if your opponent is playing extra deck, or you manage to keep one on the field) while Dogmatika Ashiyan provides recycle capability, as does sending Titaniklad the Ash Dragon from the extra deck to the GY. Nadir Servant provides another way to start this engine.
The main idea though is to use Dogmatika Ecclesia, the Virtuous to gain access to your ritual monsters - White Knight of Dogmatika and White Relic of Dogmatika - and your ritual spells - Dogmatikalamity and Dogmatikamacabre. This might require sending Herald of the Arc Light to get a ritual spell, and if Dogmatika Maximus is in hand, getting an extra deck monster to the GY sets up nicely. Diviner of the Herald is included to add another option for this part of the engine.
Salamangreat Almiraj into Secure Gardna is a quick way to get an extra deck monster in grave, especially with Dogmatika Maximus in hand as this provides further extra deck dump. Tri-Brigade Ferrijit the Barren Blossom is a good option to replace a brick in the starting hand, while Lyna the Light Charmer, Lustrous can potentially provide this too as well as disruption.
Preparation of Rites and Pre-Preparation of Rites provide consistency, but I've not figured out the ratio of ritual monsters to use in order to make these two most effective.
Dogmatika Punishment and Shaddoll Schism and Secret Village of the Spellcasters provide nice disruption while Infinite Impermanence is a good game 1 card to have which can be swapped for other hand traps if needed. Effect Veiler is good for a route into link plays as well as hand trap. The Shaddoll extra deck cards are a way to recycle the single Shaddoll Schism.
This is the first deck I've ever built myself, so feedback is more than welcome!