The most important thing in dealing with potential "red flag" issues is to identify and disclose them early in the process. USCIS and consular officials are less troubled by issues that are disclosed and dealt with early on. The second most important thing is to convince the consular adjudicator that the issue should not result in a denial of the K1 application. 

So how do you do this? Every issue is different, and there is no one size fits all solution. However, one thing is true for all issues: the issue must be overcome with solid and compelling documentary evidence. This evidence should ideally be submitted at the USCIS level but can be supplemented with further proof at the consular level.