Burning Vengeance has an ability that triggers whenever you cast a spell from your graveyard. Not everything that comes from your graveyard and ends up in play is due to casting that spell from your graveyard. It is important to know what actually triggers this ability.
Let’s start with the basics: casting a spell via its flashback cost from your graveyard will trigger this ability. This is because you are casting that spell from your graveyard; you are just paying an alternate cost. For example, casting a Geistflame from your graveyard by paying 3R will trigger Burning Vengeance’s ability. Similarly, taking advantage of Skaab Ruinator‘s ability and casting it from your graveyard will trigger this ability.
However, effects that put a card from your graveyard into play will not cause this ability to trigger. For example, if you pay 4B and play Unburial Rites from your hand, the targeted creature will be returned to play when Unburial Rites resolves. However, this is not casting a spell from your graveyard, so Burning Vengeances’s ability will not trigger. (Playing Unburial Rites via its flashback cost from your graveyard will cause Burning Vengeance’s ability to trigger, but returning the creature to play will not.)
The unearth activated ability will temporarily return a creature card from your graveyard to play. However, this is an activated ability–not casting a spell from your graveyard–so unearthing a Viscera Dragger will not trigger Burning Vengeance’s ability.