1. your form's enctype should be multipart/form-data (otherwise it does not work):

<form method="post" enctype="multipart/form-data">
...
</form>

2. You should specify upload folder (otherwise it does not work):

app.config['UPLOAD_FOLDER'] = '/path/to/the/uploads'

3. You should specify a name for your file input (otherwise it does not work):

<input type="file" name="file1">

4. you should manually save the file with file save() method:

path = os.path.join(app.config['UPLOAD_FOLDER'], file1.filename)
file1.save(path)

4. Simple full example:

import os
from flask import Flask, request

UPLOAD_FOLDER = './upload'

app = Flask(__name__)
app.config['UPLOAD_FOLDER'] = UPLOAD_FOLDER

@app.route('/', methods=['GET', 'POST'])
def upload_file():
    if request.method == 'POST':
        if 'file1' not in request.files:
            return 'there is no file1 in form!'
        file1 = request.files['file1']
        path = os.path.join(app.config['UPLOAD_FOLDER'], file1.filename)
        file1.save(path)
        return path

        return 'ok'
    return '''
    <h1>Upload new File</h1>
    <form method="post" enctype="multipart/form-data">
      <input type="file" name="file1">
      <input type="submit">
    </form>
    '''

if __name__ == '__main__':
    app.run()

5. Detailed full example: https://flask.palletsprojects.com/en/1.1.x/patterns/fileuploads/

In case you just want to upload, analyze, and display the image without saving it to storage, i.e. api and edged image analysis, this example might be a guide for you. Flaskimio

@app.route("/",methods=['GET', 'POST'])
def index():
    if request.method == 'POST':
        if 'file' not in request.files:
            print('No file attached in request')
            return redirect(request.url)
        file = request.files['file']
        if file.filename == '':
            print('No file selected')
            return redirect(request.url)
        if file and check_allowed_file(file.filename):
            filename = secure_filename(file.filename)
            print(filename)
            img = Image.open(file.stream)
            with BytesIO() as buf:
                img.save(buf, 'jpeg')
                image_bytes = buf.getvalue()
            encoded_string = base64.b64encode(image_bytes).decode()         
        return render_template('index.html', img_data=encoded_string), 200
    else:
        return render_template('index.html', img_data=""), 200


<form method="post" enctype="multipart/form-data">
    <p><input type="file" id="file" name="file"><input type=submit value=Upload></p>
    <img src="data:image/jpeg;base64,{{ img_data }}" id="img-upload" alt="img_data" class="img-upload"/>
</form>