No, some peaks are okay.
A flat line in blood sugar is only possible when you don't eat at all (fasting). All foods (especially carbohydrates) raise your blood sugar, which in itself is fine. Your body maintains a closely regulated balance. Above 7 mmol/L (from food) is not so good, this 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 responds less and less well to lower insulin concentrations. Ultimately, too often, too high, leads to too little insulin: insufficient to have an effect.
In addition, spikes in blood sugars are also observed after exercise and sports. This means that your body uses the glucose (glycogen) stored in the body. You 'burn' energy.
Finally, and this may not be so good: stress. High stress levels can cause spikes in blood sugar.