Is there a way to create an autocompletion field that shows entries from two other fields, so that when I start typing, it searches for the entry in either fields and runs the autocompletion.

FileMaker  is a relational database and as such it has to have one path at any given time. That being said, you can cheat and hack your way into other methods. So you could create another table (table C), drop all your records from table A and table B into that (into the same field), then you can search on that table and it will contain data from both sources.

I'm sure others will chime in with different solution ideas here.