What is the type advantage damage multiplier?

The bonus follows the skill's element, not the type of the Aniimo using it. To hit a target's weakness you pick a move of the element it is weak to, so a Fire Aniimo carrying a Water skill can still land 1.6x on another Fire Aniimo.

Most elements are super effective against two others. Fire hits Grass and Ice for 1.6x, Lightning hits Water and Wind, and Dark covers three: Fire, Grass and Light. Light and Dark are super effective against each other, so that matchup cuts both ways.

The penalty on the other side is steeper than the bonus is generous. Attacking into a resistance drops your damage to roughly 0.5 to 0.6 times normal, so a skill aimed the wrong way costs you more than the right one gains. There are no elemental chain reactions stacking on top of this; the multiplier is the whole effect.

When advantage is not the point

Lunara is built around the opposite case. Its passive raises its final damage by 30% when it attacks without an elemental advantage, which makes it a fit for neutral matchups where nobody else in your team has a 1.6x skill to use.

Not settled: The exact resisted multiplier is not pinned down in the current build: it is given both as 0.5 to 0.6 times and as 0.625x. Earth's second strong matchup is also unsettled, listed as both Fire and Lightning.