How can we make the flutter app to make automatic update whenever we release a new version of the app into the store. but I don't want to use the pop up to alert the user to update I want to update automatically without letting the user even know we update it.
As said in the comment, if you publish to Google Playstore or iOs AppStore, they will handle the updates for you. You just have to upload the new version (just set the release number correctly) and, when the validation is done, their system will notify/update the app. I don't know how other stores behave, but I'm guessing that's the standard behaviour now.
Instead, if you need to bypass the store functionality and perform the update "by yourself", I don't think that is gonna be a simple task. Apple simply doesn't allow installation from other sources than their store, so I fear it may be simply impossible. On Android, on the other hand, I know that's possible, but it will require some user interaction beforehand, since the "installation from unknown source" authorization must be provided to the app that downloads/opens your .apk file, and the procedure may vary from a device to another, so I fear there won't be a single mechanism that will work everywhere.
In any case, the base mechanism will probably require some HTTP GET by your app towards some webserver that will reply with the latest version: the app should then compare the received version number with its own, and then proceed to the download of the package (the URL for the download can be provided along with the latest version number). After that, you have to manage somehow to install/update the downloaded file.
I personally used this approach with Flutter on Windows 7 and newer, where there are no store constraints and I can simply run and download the .msi or .exe file for the latest version, and works just fine.