In this paragraph below, CDC recommendation is to test before flights. The paper says vaccines may not be completely effective against all variants, for all people, so preventive measures should still be in effect.
Background Rationale and Evidence for Public Health Recommendations for Fully Vaccinated People
Updated Apr. 2, 2021
Individuals may be at risk for exposure to SARS-CoV-2 before, during, and after travel. This could result in spread of the virus throughout the travel journey, at destinations, or upon returning home. Comprehensive, layered prevention measures before, during, and after travel are critical strategies to reduce the burden of travel-associated spread of SARS-CoV-2. To reduce this risk, CDC has recommended that all travelers be tested for the virus 1–3 days before departure (required for air passengers traveling to the United States from a foreign country unless they can present documentation of recovery from COVID-19 in the previous 3 months), combined with a second test 3–5 days after travel and staying home to self-quarantine for a full 7 days after travel if the post-travel test result is negative. If post-travel testing is not done, the recommendation is to extend self-quarantine to 10 days after travel.