This information comes from the official Japanese game website, and according to a translation, amiibo will unlock useful items for Zelda's adventure, as well as different colours of clothing.
"In addition to items that will be useful for your adventure, you may also be able to get different colors of clothing that can be obtained in the game."
The same page includes a full list of compatible amiibo:
Zelda amiibo compatible with Zelda: Echoes of Wisdom
- Ganondorf (Tears of the Kingdom)
- Zelda (Tears of the Kingdom)
- Link (Tears of the Kingdom)
- Zelda & Loftwing (Skyward Sword)
- Link (Link's Awakening)
- Young Link (Smash Bros)
- Urbosa (Breath of the Wild)
- Daruk (Breath of the Wild)
- Mipha (Breath of the Wild)
- Revali (Breath of the Wild)
- Link (Skyward Sword)
- Link (Twilight Princess)
- Link (Majora's Mask)
- Guardian (Breath of the Wild)
- Zelda (Breath of the Wild)
- Bokoblin (Breath of the Wild)
- Link Rider (Breath of the Wild)
- Link Bow (Breath of the Wild)
- Zelda (Wind Waker)
- Toon Link (Wind Waker)
- Link (Ocarina of Time)
- Link (The Legend of Zelda)
- Wolf Link (Twilight Princess)
- Ganondorf (Smash Bros)
- Sheik (Smash Bros)
- Toon Link (Smash Bros)
- Zelda (Smash Bros)
- Link (Smash Bros)