Note :-- It happens in default small Touch UI dialog window, not on full dialog window.
I too checked the issue in Chrome and Mozilla and yes there is a dropdown flickering issue and not on full dialog window.
I think this is a bug. Please raise the support ticket to Day care.
Could you please update the resolution here as we are also facing the same issue here on AEM 6.4 SP3. Is this got resolved?
Would really appreciate your help.
Please have team expand and review the 126.96.36.199 release notes  , in particular, search for CQ-4257440 details :
Hi Tarrant County team,
We are working internally (with your CSE) to review the issue on your PROD environment -- we will be updating the related Daycare ticket accordingly. We apologize for the lack of ticket updates -- as detailed in the recent ticket update.
Thank you so much for your quick resolution to this issue. For others with this problem, it was happening on our system due to dispatcher caching on the author.