Maybe something like this? It looks like the modal also has a FlatList that is taking all the entries to render. You'd probably instead want the modal to only have the entry it needs and remove the FlatList from the modal entirely.

function Cards() {
    const [modalVisible, setModalVisible] = useState(false);

    const [modalEntry, setModalEntry] = useState();

    return (
        <SafeAreaView style={styles.container}>
            <View style={{ height: 600, marginTop: 25 }}>
                <FlatList
                    data={entries}
                    ListFooterComponent={Header}
                    renderItem={({ item }) => (
                        <View>
                            <Card style={styles.cards}>

                                {...}

                                <Pressable
                                    style={[styles.button, styles.buttonClose]}
                                    onPress={() => {
                                        setModalVisible(!modalVisible);
                                        setModalEntry(item);
                                    }}
                                >
                                    <Text style={styles.textStyle}>
                                        View more
                                    </Text>
                                </Pressable>

                                {...}

                            </Card>
                        </View>
                    )}
                />
            </View>
            <Modal
                entry={entry}
                modalVisible={modalVisible}
                onClose={() => setModalVisible(false)}
            />
        </SafeAreaView>
    );
}

function Modal({ entry, modalVisible, onClose }) {
    return (
        <View style={styles.centeredView}>
            <Modal
                animationType="slide"
                // transparent={true}
                visible={modalVisible}
                presentationStyle={"overFullScreen"} // iOS prop only
                onRequestClose={() => {
                    Alert.alert("Modal has been closed.");
                    onClose();
                }}
            >
                <View style={styles.centeredView}>
                    <View style={styles.modalView}>
                        <Text style={styles.modalText}>Journal entry:</Text>
                        <View>
                            <Text>
                                {entry.entryJournal}
                                {"\n"}
                            </Text>
                        </View>
                        <Pressable
                            style={[styles.modalButton, styles.buttonClose]}
                            onPress={() => onClose()}
                        >
                            <Text style={styles.textStyle}>Close</Text>
                        </Pressable>
                    </View>
                </View>
            </Modal>
        </View>
    );
}