The prestige class Dragon Disciple has the feature Blood of Dragons, which states:
A dragon disciple adds his level to his sorcerer levels when determining the powers gained from his bloodline.
This specifically states Sorcerer levels; however, in a 2015 FAQ, Paizo said:
...dragon disciple's blood of dragons ability should also increase draconic bloodragers’ bloodline powers.
Now, the Blood Arcanist archetype grants the Arcanist a Sorcerer bloodline, saying:
A blood arcanist selects one bloodline from those available through the sorcerer bloodline class feature. The blood arcanist gains the bloodline arcana and bloodline powers of that bloodline, treating her arcanist level as her sorcerer level.
By the same logic that a Bloodrager is intended to be able to progress their bloodline, would the Dragon Disciple be able to progress a Blood Arcanist's bloodline?