KLM offers direct service from Amsterdam to Entebbe. I have taken this flight, originating from Atlanta and found it to be a perfect connection. We left my home town and flew to Atlanta just after noon on Monday. Left Atlanta for Amsterdam Monday night. Arrived Amsterdam Tuesday morning and later that morning left for Entebbe and arrived that same night. With British Airways for example, you leave the US Monday and do not get to Entebbe until Wednesday.

The return Entebbe, Amsterdam, USA, also has great connections.

Below is the KLM Amsterdam to Entebbe schedule (always double check as airlines change things all the time). You will need to leave the US as per this chart to make the best connection. If you leave the US Monday, Thursday, or Saturday, you fly through Nairobi to Entebbe and that can be problematic.