<li class="in">{{login_status | default('Вход')}}</li>
 <form name="form_in" method = 'post' action = '/personal_account'>
       <input type="text"  placeholder="Логин" id="log" name="login"/>
       <input type="password"  placeholder="Пароль" id="pass" name="password"/>
       <input type="submit"/>
 </form>

@app.route('/personal_account', methods=['POST'])
def welcome():
    login = request.form['login']
    password = request.form['password']
    login_status = u'Выйти'
    sidebar_login_status = 'out'
    if not validate_user(login, password):
        login_status = u'Войти'
        sidebar_login_status = 'in'
        return u'Неправильный логин!', login_status, sidebar_login_status

    # добавлено после Edit One
    user = User()
    user.id = login
    login_user(user)
    # .......

    data = get_user_data(login)
    return render_template('private.html',
                           data=data,
                           login_status=login_status,
                           sidebar_login_status=sidebar_login_status)

<a href="{{url_for('login')}}"> {{session.get('login_status', 'log in')}} </a>

from flask import Flask, session, redirect, url_for, render_template
app = Flask(__name__)

@app.route('/login')
def login():
    login_status = session.get('login_status', 'log in')
    if login_status == 'log in': session['login_status'] = 'log out'
    elif login_status == 'log out': session['login_status'] = 'log in'
    return redirect(url_for('index'))

@app.route('/')
def index():
    return render_template('index.html')

if __name__ == '__main__':
    app.secret_key = '123'
    app.run(debug=True)