I know taxi apps are becoming popular in Georgia's capital. Are there any that also work in Kutaisi?
There is a TaxiMaxim Company which also works (at least according to their web-site) in Kutaisi, they also have English web-site(among few others) interface, which I checked and is not exactly perfect, I noticed some bugs in suggestions while typing street/city names, maybe it's better in application but it should work overall. You can find application download links right on the main page.
P.S maybe this is totally irrelevant to your case but I think it is worth mentioning that taxi is one of the things that you are not gonna have problems to find in Georgia, big cities that is, such as: Tbilisi, Kutaisi or Batumi. Basically every 3rd, 4th car is a taxi and it's quite cheap :)