I think his actions are pretty terrible but luckily the the 1A still applies as it should to his actions https://www.itv.com/news/2019-05-10/danny-baker-being-investigated-over-racist-royal-baby-tweet/
Ok
The First Amendment has nothing to do with actions in other countries by non-Americans.
This has nothing to do with first amendment. First, his employer fired him because of lack of judgment. In media they do this all the time. After all you are employed at will. Second police got an allegation report and they must investigate by law. Most likely they will drop it in one hour.
Third it happened in the UK
https://www.youtube.com/watch?v=p3I1YDbSLQk