There's no 100 percent proof that eating cinnamon speeds up your metabolism but when you do eat cinnamon your body will use more energy to process the spice and cinnamon through your body.
So since your body uses more energy to process the cinnamon spices then it's likely that eating cinnamon does help speed up your bodies metabolism.
Cinnamon is very health as well and can help you lose weight, lower your blood pressure, lower your blood sugar levels, may help prevent diabetes and helps to detox your body.
Cinnamon can also help keep your heart healthy and can reduce your risk of a heart attack, heart disease, strokes etc.
I love to add some cinnamon to my tea or coffee and my blood pressure has been lowered as a result when I used to suffer from high blood pressure.
Just don't eat cinnamon directly without putting it in foods or in a drink because eating cinnamon off a spoon can choke you and close off your airways which can be deadly.