He immediately fell flat on his back.

【翻译】他立刻仰面平躺着。

【分析】fall flat：fall是系动词，flat是形容词。看作系表结构也可，看作固定短语也可。

fall 用作系动词，多跟一些偶然性的不可预期的形容词连用：

fall ill   生病

fall asleep  入睡

fall flat  失败；失效

关于on his back 这个短语的用法和意义，分析如下：

从on one's back 看on 的一个特殊用法

有本书上说 on one’s back 有两个意思：一是表示“在背上”，二是表示“仰着身子”。如何理解它表示“仰着身子”的含义呢？

这是一个很有意思的问题。介词on表示位置时，意为“在......上面”，指两个物体接触。on one’s back指“（物体）在人的后背上”。例如：

1. The tourist carried a pack on his back.  观光旅行者背了个包。

2. The old man bent with a heavy burden on his back.  老人因背著重负而弯腰。

3. The burden on his back seemed to be crushing him to the earth.  他背上的重负似乎要把他压倒在地。

4. I patted him on his back, and told him what a brave boy he was.  我拍了拍他的后背，称赞他是个勇敢的孩子。

5. The man with a sack on his back is a farmer.  背着一个大布袋的人是个农民。

此外，on 还有一个重要的用法，就是，“（身体重量）由（某部位）支撑”： You use on to say what part of your body is supporting your weight.  

这类短语名词一般是人的身体部位，与lie, stand, stay, remain, fall，be等动词连用。on one’s back 当跟动词lie连用时，即lie on one’s back表示“仰着身子”，这时候的on，即表示“由......支撑”。这就是你句子中的用法。

例如：

1. He continued to lie on his back and look at the clouds. 他仍旧仰卧着，望着天上的云彩。

2. He raised himself on his elbows, squinting into the sun. 用胳膊肘支起身子，眯着眼睛看了看太阳。

3. The man was on her hands and knees in the bathroom. 那个人趴在浴室的地上。

4. When he woke up, he tried to stand on his feet, but he failed. 当他醒来要努力站起来时,但他失败了。

5. The wind was so strong that little Hans found it difficult to stand on his feet. 风这样猛烈，小汉斯感到自己站也站不住。

6. In a busy gasoline station, the attendant is on his feet all day. 在忙碌的加油站，工作人员整天都走动着。

7. After six whiskies Harry was finding it difficult to stay on his feet. 6杯威士忌下肚，哈里两腿站不住了。

8. He stood on his head to make the baby laugh. 他倒立着使婴儿发笑。  

9. In return for this, the beggar stood on his head and sang songs. 这个乞丐倒立着唱了几支歌作为报答。

10. He lay on his stomach, making an earnest business of sleeping. 他这会儿趴在床上，看样子好象睡得正熟呢。

11. He crawled on his hands and knees for 100 metres. 他爬行了100米。

12. He lay on his back, his hands behind his head. 他仰卧着，双手扣着后脑勺。

13. He tried to stand on his head but couldn't. 他试图倒立，但没有成功。

14. The old man is not steady on his legs. 这位老人站不稳。

15. He was lying on his chest and then turned over to look up at the sky.  他先是趴着，后来翻身仰面朝天。