这个蛋糕有多少卡路里？ CORRECT! Is 张 the measure word for calorie? NO, 張 is the measure word for paper, calorie is not a common noun, it's a 單位名詞(just like km, kg, joule.etc..it's always use with numbers, even 千卡 "千"is number also.)，you don't have to put measure word before it, you say 這個蛋糕有多少卡路里 is absolutely right!

这个蛋糕有多少卡路里？ How many calories in this cake? If you said this everybody would know exactly what you're saying, correct! You would hear people often say the following in daily life: 这个蛋糕有多少热量？ 这个蛋糕有多少大卡？ I don't understand what you're getting at in terms of the measure word for calorie, it seems the only measure word commonly used is 千（卡）I can think of at the moment.

卡路里(calorie)是能量单位，我认为它本身也可以被当作measure word来用。 e.g. Percent Daily Values are based on a 2,000 calorie diet. 每日所需标准百分比，是以2000卡路里的食物为计算标准。 如果一定要加一个量词，用“个”勉强可以。 如：人的热能消耗每天需要大约2000个卡路里