Will a refusal for UK visitor's visa have any impact on a US visitor's visa application result?

The UK is part of a protocol between the USA and the affluent Commonwealth to share immigration related data. This includes biometrics, photographs, current name, previous names, passport scans, previous applications, and visa history. For the USA, it means the information is sent to the Department of Homeland Security where it is kept on file more or less permanently but for straightforward cases 12 years (75 years is the maximum).

So the USA would have a record of your brother's application history. Of course none of the protocol members will disclose how the data is used and there are no publically available statistics on the extent to which a pejorative history in one country can influence decisions in another country. This makes the "official" answer to your question indeterminate.

From a purely personal point of view, when I was in practice I saw numerous cases of people who had been refused USA visas go on to successfully apply for visas in a Commonwealth regime and vice-versa. It seems to happen most often when the person has been refused, but has no performance issues in their history. When the person has had a bookable performance issue (like when they entered illegally or they were caught overstaying and removed at public expense, or when they were caught working and removed), then the effect seems more pronounced (but not certain).

For an extreme case, I had a person who had been refused in both countries. I was able to explain that the decision-maker was a perfect ass and after that the person was able to get visas in both countries going forward on multiple occasions. That may not work in all cases, but they are aware that the decision-making systems are not perfect.

Based upon what you wrote, your brother was refused a UK settlement visa under Paragraph 317. This is taken quite seriously in the UK as a show-stopper, but there's no performance issues associated with it that would necessarily alarm another country, especially if your brother did not have a family infrastructure in another country. There's no crime in applying for a visa from a foreign location.

If your brother needs to visit the USA, he should go ahead and apply. If he qualifies, it will make a step forward in establishing his credibility with the UK. And with continued success over a period of time, for example Canada, Australia and so on, the UK decision makers will look favourably on his case.

Summary: you can reliably assume that the USA has a file on your brother's UK history. In the absence of breach or criminal activity, there's no reason to believe an application will be refused outright. And the caveat is that a USA legal specialist will be able to examine all of your brother's materials and give you a better reading on it.

NOTE: the protocol has been formulated and is working on a day-to-day basis, but neither the US Senate nor the UK Parliament have ratified it as a treaty.