Dice can be used to reroll the following:
Goals: if you don't like a currently available goal you can spend dice to change it
Bird selection: while in a battle if you don't like the birds offered, you can use a dice to reroll the options
Charms: if after a battle, you don't like the charms offered, you can usea dice to reroll the options
Events: when building your flock, you can use a dice to reroll the offered birds