I’m omitting that I’m married to an American man in my fiancée visa application to the UK. Will this be a problem? Do they cross-reference databases? [closed]

Do they cross-reference databases?

The first question is whether or not the US federal government even knows about your marriage. If you've never applied for a spouse visa to the US or otherwise notified the federal government about your situation (such as through a joint tax return), it's possible that there isn't a record of your marriage in any federal databases. If there is in fact a record, the UK could probably look it up without much fuss thanks to the Five Eyes agreement.

However the above is absolutely irrelevant: you as a visa applicant should always strive for 100% honesty or avoid applying for a given visa altogether. If the UK ever finds out you've lied on your application you can expect a long ban from the country in the future. The risk is simply not worth the potential time savings - finish up your divorce in the US and then come to the UK without having to lie to anyone.

They won’t need to check any databases. You have to prove that you’re free to marry, typically you’ll need to provide, for example, a sworn affidavit / Declaration of Single Status (no impediment) signed and stamped by a notary public or equivalent in your country of residence.