Bundle Kit is compatible with third-party upsell apps under specific conditions.
There are two aspects of compatibility: frontend and backend.
For the frontend, Bundle Kit is fully compatible and will not conflict with any third-party apps that modify the storefront or product details page.
To learn more: Can Bundle Kit impact my store theme or page performance?
For the backend, Bundle Kit is fully compatible with third-party apps that upsells products via adding the dummy (bundle) product to the native cart, and is partially compatible with apps that upsells products via bypassing the cart and directly creating an order.
To understand why: Bundle Kit edits the Shopify order to add bundle items as line items. However Shopify marks an order as uneditable if the order is directly created by a third-party app.
This means Shopify will prevent both Bundle Kit and even the merchant to edit the order (to add the bundle items as line items).
Learn how to handle this Shopify limitation by reading: Handling uneditable orders