How do Chinese spell English words over the phone?
Even for educated Chinese people who know English fairly well, they do not use the same method that native English speakers use (the one mentioned in your question).
The common methods Chinese use include:
1 - Read a small sequence of letters from the alphabet that contains the letter in question.

“Theodore怎么拼？”
“T-H-...”
“等一下，是T还是P”
“T，R-S-T的T&quot;

2 -  Prefix the letter with its ordinal number in the alphabet. This is borrowed from school as it's how teachers and students read answers of choice questions. It is commonly used for A-D but not very common for letters after D.

“最后一个字母是二B还是四D？”
“四D。”

(Make sure when you read “2B&quot;, B is in prominent falling tone, to distinguish from the swearing word &quot;二逼&quot; where the second character reads bi1. Of course students often make joke out of these homonyms.)
3 - Describe the shape or some other distinctive properties of the letter.

“G还是J？” (It's very common for Chinese people to confuse the pronunciations of these two letters.)
“J，勾儿。” (It's referring to the shape of the letter AND also it's the urban name of the letter in poker games.)

If you do need to spell some English word over the phone with a Chinese, chances are the person is a service personnel, receptionist or secretary, with whom these methods work quite well, as per my personal experience.