Is it possible to flash an app via custom recovery? If it is, will it become a system app? I wanted to have an app as a system app without rooting it. I was wondering if it's possible to flash/install an app through custom recovery as we do with Gapps and other stuff.
So, I came up with an idea to flash it via recovery, but I don't know whether it will work or not. If not, is there any other way to make an app a system app without rooting?
Yes, it is definitely possible and has been done many times. The method to do so is explained in this article.
Briefly, the main steps from the provided link are following:

Download any similar zip template
Extract it; there will be 2 folders - META-INF &amp; system
Make a folder with the name app inside the system folder
Paste your APK files in the app folder
Zip META-INF &amp; system into a file
Flash it