No, as mentioned in an earlier post, not OK for a US-registered aircraft to operate commercially under a Guernsey AOC, or at all if it is Part-91
Also, as Channel Jets is a Guernsey AOC, and Guernsey is non-UK and non-EU, they can't operate even a 2-REG aircraft commercially to/from UK or EU without a permit from the Authorities at both ends (e.g. a flight from France to UK would need a permit from both France and the UK)