Flutter api reloads every navigation

You need to to separate your api call from your ui. That way your api will only get called when you want it to. I recommend using some kind of external state management library, such as Provider, BLoC, or RxDart. Flutter will rebuild a widget anytime it wants to, beyond when you trigger it.

you passed getWord() as a function to you future builder so each time the widget get rebuilt, it is called.

To solve that, declare a variable Future<Word> getWordFuture ; , Inside initState assign getWordFuture = getWord(); and use getWordFuture in the Future builder.

import 'dart:async';
import 'dart:convert';

import 'package:flutter/material.dart';
import 'package:http/http.dart' as http;

import 'models/Word.dart';

class WordListPage extends StatefulWidget {
  WordListPage(Key k) : super(key: k);

  @override
  _WordListPageState createState() => _WordListPageState();
}

class _WordListPageState extends State<WordListPage> {
  Future<List<Word>> data;
  bool isSearching = false;
  TextEditingController myController = TextEditingController();
  List<Word> _words = List<Word>();
  List<Word> _wordsForDisplay = List<Word>();
  var keyListPage = PageStorageKey('list_page_key');
Future<List<Word>> getWordFuture = Future<List<Word>> ; //1

  Future<List<Word>> getWord() async {
    var response = await http.get("myAPIurl");
    var _words = List<Word>();

    _words = (json.decode(utf8.decode(response.bodyBytes)) as List)
        .map((singleWordMap) => Word.fromJsonMap(singleWordMap))
        .toList();
    return _words;
  }

  @override
  void initState() {
   getWordFuture = getWord(); //2
    getWord().then((value) {
      setState(() {
        _words.addAll(value);
        _wordsForDisplay = _words;
      });
    });
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: myFutureBuilder(),
      appBar: AppBar(
        leading: Center(
          child: RichText(
            textAlign: TextAlign.center,
            text: TextSpan(
              style: DefaultTextStyle.of(context).style,
              children: <TextSpan>[
                TextSpan(
                  text: 'Total',
                  style: TextStyle(
                    decoration: TextDecoration.none,
                    fontSize: 10,
                    color: Colors.white,
                  ),
                ),
                TextSpan(
                  text: '\n${_words.length.toString()}',
                  style: TextStyle(
                    decoration: TextDecoration.none,
                    fontWeight: FontWeight.bold,
                    color: Colors.white,
                    fontSize: 12,
                  ),
                ),
                TextSpan(
                  text: '\nLetter',
                  style: TextStyle(
                    decoration: TextDecoration.none,
                    color: Colors.white,
                    fontSize: 10,
                  ),
                ),
              ],
            ),
          ),
        ),
        centerTitle: true,
        title: !isSearching
            ? Text('My Title')
            : TextField(
                autofocus: true,
                style: TextStyle(color: Colors.white),
                controller: myController,
                onChanged: (value) {
                  value = value.toLowerCase();
                  setState(
                    () {
                      _wordsForDisplay = _words.where(
                        (word) {
                          var wordTitle = word.word.toLowerCase();
                          return wordTitle.contains(value);
                        },
                      ).toList();
                    },
                  );
                  setState(
                    () {
                      _wordsForDisplay = _words.where(
                        (word) {
                          var wordPronounce = word.pronunciation.toLowerCase();
                          return wordPronounce.contains(value);
                        },
                      ).toList();
                    },
                  );
                },
                decoration: InputDecoration(
                  isCollapsed: true,
                  icon: Icon(
                    Icons.menu_book,
                    color: Colors.white,
                  ),
                  hintText: 'Search',
                  hintStyle: TextStyle(color: Colors.white),
                ),
              ),
        actions: [
          isSearching
              ? IconButton(
                  icon: Icon(Icons.cancel_outlined),
                  onPressed: () {
                    setState(
                      () {
                        this.isSearching = false;
                        myController.clear();
                        _wordsForDisplay = _words.where(
                          (word) {
                            var wordTitle = word.word.toLowerCase();
                            return wordTitle.contains(wordTitle);
                          },
                        ).toList();
                      },
                    );
                  },
                )
              : IconButton(
                  icon: Icon(Icons.search_sharp),
                  onPressed: () {
                    setState(
                      () {
                        this.isSearching = true;
                      },
                    );
                  },
                ),
        ],
      ),
    );
  }

  FutureBuilder<List<Word>> myFutureBuilder() {
    return FutureBuilder(
      //future: getWord(),
      future:getWordFuture,
      builder: (context, AsyncSnapshot<List<Word>> snapshot) {
        if (snapshot.hasData) {
          return myWordListView(snapshot);
        } else {
          return Center(
            child: CircularProgressIndicator(),
          );
        }
      },
    );
  }

  ListView myWordListView(AsyncSnapshot<List<Word>> snapshot) {
    return ListView.builder(
      itemCount: _wordsForDisplay.length,
      itemBuilder: (context, index) {
        return ExpansionTile(
          title: Text(
            _wordsForDisplay[index].word,
            style: TextStyle(fontWeight: FontWeight.w500, fontSize: 16.0),
          ),
          subtitle: Text(
            snapshot.data[index].pronunciation[0].toUpperCase() +
                snapshot.data[index].pronunciation.substring(1),
          ),
          leading: CircleAvatar(
            child: Text(snapshot.data[index].word[0]),
          ),
          children: [
            Row(
              mainAxisAlignment: MainAxisAlignment.center,
              children: [
                Container(
                  width: MediaQuery.of(context).size.width,
                  child: Padding(
                    padding: const EdgeInsets.symmetric(
                        vertical: 7.0, horizontal: 19.0),
                    child: RichText(
                      text: TextSpan(
                        style: DefaultTextStyle.of(context).style,
                        children: <TextSpan>[
                          TextSpan(
                            text: snapshot.data[index].word + ' : ',
                            style: TextStyle(fontWeight: FontWeight.bold),
                          ),
                          TextSpan(text: snapshot.data[index].meaning),
                        ],
                      ),
                    ),
                  ),
                ),
              ],
            ),
          ],
        );
      },
    );
  }
}