After setup Flutter project code from Git repository.  To open android module right click on project and generally it should show as Flutter menu option- > Open Android module in Android Studio option.

At times, There is a chance that Flutter option is disabled as shown below

and your only option to open android module is Go to Android studio Menu File -> Open -> then select android module. You cannot simply start using Flutter menu option.

To resolve this issue, 

Step1: Right click on android module then Select New -> File

Step2:  Enter File name as your <projectname>_android.iml

Step3: In this <projectname>_android.iml file, paste below code.

<?xml version="1.0" encoding="UTF-8"?>
<module type="JAVA_MODULE" version="4">
<component name="NewModuleRootManager" inherit-compiler-output="true">
<exclude-output />
<content url="file://$MODULE_DIR$">
<sourceFolder url="file://$MODULE_DIR$/lib" isTestSource="false" />
<sourceFolder url="file://$MODULE_DIR$/test" isTestSource="true" />
<excludeFolder url="file://$MODULE_DIR$/.dart_tool" />
<excludeFolder url="file://$MODULE_DIR$/.idea" />
<excludeFolder url="file://$MODULE_DIR$/.pub" />
<excludeFolder url="file://$MODULE_DIR$/build" />
</content>
<orderEntry type="sourceFolder" forTests="false" />
<orderEntry type="library" name="Dart SDK" level="project" />
<orderEntry type="library" name="Flutter Plugins" level="project" />
<orderEntry type="library" name="Dart Packages" level="project" />
</component>
</module>

That’s it.

Now you can see the Flutter option enabled in when right click on Project  and you can Open Android module easily.

Hope it helps.