I'll walk you through each step:

### 1. Add a button

Here's a simple HTML button:

```html
<button id="openPopup">Open Popup</button>
```

### 2. Implement a popup

We can use Bootstrap's Modal component for this. Make sure to include Bootstrap's CSS and JS files in your template if you haven't already:

```html
<!-- Include Bootstrap CSS -->
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/4.5.2/css/bootstrap.min.css" rel="stylesheet">

<!-- Include Bootstrap JS and Popper.js -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.5.2/js/bootstrap.min.js"></script>
```

Modal HTML:

```html
<div class="modal fade" id="sliderModal" tabindex="-1" role="dialog">
  <div class="modal-dialog" role="document">
    <div class="modal-content">
      <div class="modal-header">
        <h5 class="modal-title">Select Value</h5>
        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
          <span aria-hidden="true">&times;</span>
        </button>
      </div>
      <div class="modal-body">
        <input type="range" id="rangeSlider" min="500" max="15000" value="500">
        <span id="sliderValue">500</span>
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-primary" id="confirmButton">OK</button>
        <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>
      </div>
    </div>
  </div>
</div>
```

### 3. Slider interaction

Using JavaScript, we can show the modal when the button is clicked, and display the slider's value:

```javascript
document.getElementById('openPopup').addEventListener('click', function() {
    $('#sliderModal').modal('show');
});

document.getElementById('rangeSlider').addEventListener('input', function() {
    document.getElementById('sliderValue').textContent = this.value;
});
```

### 4. Implement the POST request logic

Finally, using AJAX, you can make the POST request:

```javascript
document.getElementById('confirmButton').addEventListener('click', function() {
    let sliderValue = document.getElementById('rangeSlider').value;

    $.ajax({
        type: "POST",
        url: "/your_endpoint",  // replace with your Flask route
        data: {
            value: sliderValue
        },
        success: function(response) {
            // handle success
            $('#sliderModal').modal('hide');  // close the modal
        },
        error: function(error) {
            // handle error
        }
    });
});
```

In your Flask app, handle the POST request:

```python
from flask import Flask, request, jsonify

app = Flask(__name__)

@app.route('/your_endpoint', methods=['POST'])
def handle_post():
    value = request.form.get('value')
    # Do something with the value
    return jsonify(status="success")
```

With these steps, when you click the "Open Popup" button, a modal will open with a slider. After adjusting the slider and clicking "OK", a POST request will be made to your Flask app with the selected value. Adjust the endpoint and any other necessary details accordingly.
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