score:2
Here's some general advice:
Your inclination to disclose your earlier rejection is correct. It's never a good idea to conceal anything; the cost of getting found out is likely to be very high.
The 214(b) rejection seems to indicate that the evaluating officer was unconvinced that you were planning to leave the country. The UK also issues visa rejections for that reason, so they may look more closely at your intention to leave the UK than they otherwise would. The good news is that people can and do overcome such a rejection with a new application that offers more convincing evidence of intention to leave. Presumably, the UK would not give more weight to a US rejection than they would to a UK rejection, so, as long as your evidence is solid, the earlier rejection should not disqualify you from receiving a visa.
If you no longer have documentary evidence of your earlier visa rejection from the US, that shouldn't work against you. Just disclose the rejected application, including the reason you were given for the rejection.
Most importantly, be careful to document your intention to return to your home country. Evidence of prior travel outside your country, if any, will work in your favor, since you obviously returned. Also, evidence of strong ties to your country is helpful. This could be evidence of a stable job with good pay (which you seem to have), of a spouse and/or children (or, if you have none, of other close relatives) who will remain in your home country during your trip, or of your home, especially if you own it.