Is it dangerous to take amlodipine and propranolol together?

There is a moderate interaction between both medications, moderate meaning:

Moderate Moderately clinically significant. Usually avoid combinations; use it only under special circumstances.

Interactions between your drugs
Moderate
propranolol amLODIPine
Applies to: propranolol, amlodipine

Propranolol and amLODIPine may have additive effects in lowering your blood pressure and heart rate. You may experience headache, dizziness, lightheadedness, fainting, and/or changes in pulse or heart beat. These side effects are most likely to be seen at the beginning of treatment, following a dose increase, or when treatment is restarted after an interruption. Let your doctor know if you develop these symptoms and they do not go away after a few days or they become troublesome. You may need a dose adjustment or more frequent monitoring by your doctor to safely use both medications. Avoid driving or operating hazardous machinery until you know how the medications affect you, and use caution when getting up from a sitting or lying position. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.

There are also food-drug interactions, click on the link to access the full interaction report:

Source and more information:
https://www.drugs.com/interactions-check.php?drug_list=172-0,1956-0

Do speak with your if you have doubts/questions regarding the interactions.