How do I show an empty state?

Pass ListEmptyComponent through flatListProps. The dropdown forwards it to the underlying FlatList, which renders it when the current (possibly filtered) list is empty.

import { Text, View } from 'react-native';
import { Dropdown } from '@carlos3g/element-dropdown';

<Dropdown
  search
  data={data}
  labelField="label"
  valueField="value"
  flatListProps={{
    ListEmptyComponent: () => (
      <View style={{ padding: 16 }}>
        <Text>No matches.</Text>
      </View>
    ),
  }}
  onChange={(item) => setValue(item.value)}
/>;

Works for both "data is empty to begin with" and "search filtered everything out".

Every other FlatList prop is available the same way — ListHeaderComponent, ItemSeparatorComponent, initialNumToRender, etc.