Hi
You question is actually divided into two parts:
1. AEM-RDBMS intigration or getting value from RDBMS into AEM.
2. Autocomplete feature
For part 1, please refer to these helx articles
Link:- https://helpx.adobe.com/experience-manager/using/querying-persisting-cq-data-mysql.html
// here we are Querying and Persisting Adobe AEM data into MySQL and can do Vice-verse
Link:- https://helpx.adobe.com/experience-manager/using/creating-cq-web-application-uses.html
//Creating an Adobe CQ web application that uses MySQL
For Part 2:-
What you can do is, fetch the data from Mysql and save it at JCR level. Now, we can create a Custom Search component (Many Jquery plugins are available for search and Auto complete) which will consult only data from particular Ajex call. This data can be cached in dispatcher so next time when we query the data we can use cached data. Autocomplete thing can be achieved easily by Jquery/
Dispatcher :- https://docs.adobe.com/docs/en/dispatcher.html
Dispatcher :- https://docs.adobe.com/content/docs/en/dispatcher/disp-config.html
AEM Jquery Component:- https://helpx.adobe.com/experience-manager/using/custom-carousel-components.html
Jquery Demo Autocomplete :- https://jqueryui.com/autocomplete/
AutoComplete Jquery Via AJEX:- https://www.sitepoint.com/10-ajaxjquery-autocomplete-tutorial-examples/
HTTP Cache can also be an option for caching :-https://adobe-consulting-services.github.io/acs-aem-commons/features/http-cache.html
I hope this could be of some use to you.
Thanks and Regards
Kautuk Sahni