According to Amazon Japan, the upcoming Alm and Celia amiibo will allow players to access special dungeons. The excerpt from the website was translated to state the following information:
The game supports the Alm and Celica Amiibo released at the same time; with them, you can challenge a special dungeon.
Although the context is a bit vague, the information does seem to imply that the main purpose of these amiibo is to unlock a special challenge within the game. If more information is provided, it will be posted here on the site.