All these verbs are difficult to remember and hard to use even for native English speakers(Past participle of drink comes to mind).
Brung is used as the past participle of Bring but is much less common than Brang as the past participle.
The reason for this could be because of Sing, Sang, Sung.
Bring sounds similar to sing and sometimes words that sound similar, follow the same rules (flow->flew, throw->threw.)
This is not the case for the verb Bring. The standard past simple and past participle is Brought.