You should be doing tax returns in the UK and the US, but any tax you pay in the UK will be refunded in the US. As you are non-resident in the UK you don't have to pay tax. Either you pay it, then reclaim it each year, OR you arrange to have the agency pay you the full amount without tax deducted.
Either way you have to declare it on UK & US tax return. Your US tax return allows for you to write off a certain amount of the value of the property to allow for wear and tear.
To know whether you should be keeping the flat or selling it, you need to think about how likely you are to remain in the US for the rest of your life.
UK house prices rise faster than US ones. If you sell your flat in the UK you may never be able to buy back into the UK again, or at least not without a massive downsizing. This becomes more true the longer you remain in the US. Of course, once your kids have grown up, the downsizing issue isn't as important, or you may resettle somewhere relatively cheap rather than Brighton.
So - if you don't think you'll want to buy a family home in the southern half of the UK in the next 15 years, then selling the flat would be quite sensible if it allows you to buy a good home where you live.
If you think you'll want/need a place to come back to in the UK you should think about keeping it.
Any maths you do to try and help you decide is, of course, based on the current situation. That could change in a heart beat. No-one can predict the future, so too much analysis is just confusing, IMO.