this is an example of how to move MapView.Marker smoothly by using Animated API and Easing...

Animated MapView with Marker.Animated

import React, { Component } from 'react';
import {
  StyleSheet,
  Text,
  View,
  Dimensions,
  Animated,
  Easing,
} from 'react-native';

import MapView, {Marker} from 'react-native-maps';

const {width, height} = Dimensions.get('window');
const ASPECT_RATIO = width / height;
const LATITUDE_DELTA = 0.0024524938278069897, LONGITUDE_DELTA = LATITUDE_DELTA * ASPECT_RATIO;

const styles = StyleSheet.create({
    flexbox:{
        flex: 1,
    },
    adjustCenter:{
        justifyContent: 'flex-end',
        alignItems: 'center',
    },
    backdrop:{
        backgroundColor: '#38b7ed',
    },
    welcome: {
        fontSize: 20,
        textAlign: 'center',
        margin: 10,
        fontWeight: '700',
    },
    instructions: {
        textAlign: 'center',
        color: '#333333',
        marginBottom: 5,
    },
    map: {
        ...StyleSheet.absoluteFillObject,
    },
});

class WorldMap extends Component {

    constructor(props){
      super(props);
      this.state = {
          timestamp: 0,
          region: new MapView.AnimatedRegion({
              latitude: 0,
              longitude: 0,
              latitudeDelta: 0,
              longitudeDelta: 0,
          }),
          coordinate: new MapView.AnimatedRegion({
              latitude: 23.772046,
              longitude: 90.3600703
          }),
          accuracy: 0,
          heading: 0,
          speed: 0,
          altitude: 0
      };
    }

    watchId: ? number = null;

  componentWillMount(){    
    navigator.geolocation.getCurrentPosition(
        (position) => {
              var date = new Date(position.timestamp);
              var hours = date.getHours();
              var minutes = date.getMinutes();
              var seconds = date.getSeconds();

              var lat = parseFloat(position.coords.latitude), lon = parseFloat(position.coords.longitude);
              var markerPos = {
                  latitude: lat,
                  longitude: lon
              };
              const {coordinate} = this.state
              coordinate.timing({
                  latitude: 23.772290,
                  longitude: 90.3600850,
                  duration: 2000,
                  easing: Easing.linear,
              },).start();
              this.setState({
                  timestamp: hours + ':' + minutes + ':' + seconds,
                  region: {
                      latitude: lat,
                      longitude: lon,
                      latitudeDelta: LATITUDE_DELTA,
                      longitudeDelta: LONGITUDE_DELTA
                  },
                  coordinate,
                  accuracy: position.coords.accuracy,
                  heading: position.coords.heading,
                  speed: position.coords.speed,
                  altitude: position.coords.altitude
              });
          },
          (error) => alert(JSON.stringify(error)), {enableHighAccuracy: true, timeout: 20000, maximumAge: 3000}
      );
      this.watchId = navigator.geolocation.watchPosition(
          (position) => {
              var date = new Date(position.timestamp), hours = date.getHours(), minutes = date.getMinutes(), seconds = date.getSeconds();

              var lat = position.coords.latitude, lon = position.coords.longitude;
              var markerPos = {
                  latitude: lat,
                  longitude: lon
              };
              const {coordinate} = this.state;
              coordinate.timing({
                  latitude: 23.772290,
                  longitude: 90.3600850,
                  duration: 2000,
                  easing: Easing.linear,
              },).start();
              this.setState({
                  timestamp: hours + ':' + minutes + ':' + seconds,
                  region: {
                      latitude: lat,
                      longitude: lon,
                      latitudeDelta: LATITUDE_DELTA,
                      longitudeDelta: LONGITUDE_DELTA
                  },
                  coordinate,
                  accuracy: position.coords.accuracy,
                  heading: position.coords.heading,
                  speed: position.coords.speed,
                  altitude: position.coords.altitude
              });
          },
          (error) => alert(JSON.stringify(error)), {enableHighAccuracy: true, timeout: 20000, maximumAge: 3000, distanceFilter: 2}
      );
    }

    componentWillUnmount(){
        navigator.geolocation.clearWatch(this.watchId);
    }


    render(){
        console.log(this.state.coordinate);
        return(
            <View style={[styles.flexbox, styles.adjustCenter, styles.backdrop]}>
                <MapView
                style={styles.map}
                region={{
                    latitude: 23.772046,
                    longitude: 90.3600703,
                    latitudeDelta: LATITUDE_DELTA,
                    longitudeDelta: LONGITUDE_DELTA,
                }}
                showsPointsOfInterest={true}
                pitchEnabled={true}
                zoomEnabled={true}
                showsBuildings={true}
                showsTraffic={true}
                showsIndoors={true}
                showsScale={true}
                toolbarEnabled={true}
                showsUserLocation={true}
                loadingEnabled={true}
                loadingIndicatorColor='#6600ff'
                onRegionChange={this.onRegionChange}
                >
                    <Marker.Animated                        
                        coordinate={this.state.coordinate}
                        pinColor={'coral'}
                        title={'title'}
                        description={'description'}/>
                    </MapView>
            </View>
        );
    }
}

export default WorldMap;