I don't know about the Union Jack, but the Stars and Stripes are not to be worn as an article of clothing. I don't believe that there is any law forbidding such behavior, but the custom has always been that one simply doesn't do such things.
Knowing the conservative bent of the R&A, as well as the USGA, I wouldn't be surprised if either of them made a fuss over such a breach of protocol. In fact, rather than showing a love of country, such use of the national flag actually shows a lack of respect for one's country's traditions. Perhaps that is why the R&A protested at bit.
Do you really think that anyone will pay that much money for a pair of trousers? For the contribution to the hospital, I would hope so, but I really doubt it.