Are Frequently Bought Together's discounts compatible with other app discounts or automatic discounts?

Generally the Shopify Discount system only allows one discount per order. There are a few cases where two or more discounts can be combined, as explained in the Shopify documentation at

For that reason, if you have any other app that creates discounts or you have configured automatic discounts in your store, they might interfere with each other.

Every time a discount is applied to an order, it erases any previous discount. 

If you add a discounted bundle with Frequently Bought Together and then another app adds another discount, the Frequently Bought Together discount will be removed.

Likewise, if another app adds one discount to the shopping cart and then a discounted bundle is added by Frequently Bought Together, the other app discount will be removed.

Same happens if a discount code is entered manually during the checkout process, it erases all previous discounts:

Finally, automatic discounts override discount codes so, if the order matches the criteria of a configured automatic discount, the Frequently Bought Together discount will be removed.

Please note that these are all limitations of the Shopify Discount system and we cannot change it from our side because these rules are imposed by the Shopify Platform.