No, some peaks are totally fine:
A flat line in blood sugar levels is only possible, when not eating at all (fasting). All foods (especially carbohydrates) increase your blood sugar levels, which is fine. Your body provides a closely regulated balance. Above 8 mmol/L (due to eating) is not so good, it means that the body has to make more insulin to compensate for that blood sugar peak. If that happens too often, the pancreas has to work too hard to make large amounts of insulin each time. As a result, the pancreas becomes less productive and/or the body becomes less and less good at responding to lower insulin concentrations. Ultimately, too often, too high, results in either too little insulin: insufficient to have an effect or that insulin is produced, but that the body needs much more to respond.
Additionally, peaks in blood sugars are also observed after exercise and sports. This means, your body uses its glucose (glycogen) stored in the body. You 'burn' energy.
Lastly, and this might be not so good: stress. High levels of stress can cause peaks in blood sugar levels.