Presumably you've used your EXP privileges to get seats all lined up. If so then allow an extra minute or two to check-in at AMS, most people are using this way to deal with the USA paperwork. You could have a look at the VeriFLY and SalesForce threads to check you've done all you need to do, and by all means use the direct SalesForce link purely for the LHR-DEN service. As mentioned in the thread, the MMB link doesn't work well with connections, you get one shot at it only, so it's better to use the direct link and get it right first time.
The other thing to try is checking in via the App or main website, depending on what you've used already.
It's really only a nuisance for those who are hand baggage only, since if checking in luggage it's pretty seamless.
https://digitalboarding.force.com/BA...ionEmbarque_BA