-2
#div-header {
    display: flex;
    flex-flow: row wrap; /*abreviação de flex-direction e flex-wrap*/
    align-items: center;
    justify-content: space-between;
}
<header>
            <div id="div-header">
                <div id="logo">
                    <a href="http:#"><img src="#" alt="logo" /></a>
                </div>
                <nav class="nav">
                    <div class="links">
                        <a href="#">Frases</a>
                        <a href="#">Top autores</a>
                        <a href="#">Recentes</a>
                        <a href="#">Livros</a>
                    </div>
                    <button id="btn">show e hidden</button>
                </nav>
                <div id="header-search">
                    <form id="ent-search" action="#">
                        <div id="div-busca">
                            <input id="input-search" type="text" placeholder="Pesquisar...">
                            <button id="search-button" type="submit">Buscar</button>
                        </div>
                    </form>
                </div>
            </div>
        </header>
Please clarify your problem or provide additional details in order to highlight exactly what you need. The way it’s written these days it’s hard to tell exactly what you’re asking.
–