While there is no flavor-specific version of the build task, there are flavor-specific versions of the assemble and install tasks. assemble will create the APK; install will install it on devices/emulators.

For example, in this sample project, I define two product flavors (chocolate and vanilla) and three total build types (debug, release, and mezzanine).

Running gradle tasks shows, among others:

Build tasks
-----------
assemble - Assembles all variants of all applications and secondary packages.
assembleChocolate - Assembles all builds for flavor Chocolate
assembleChocolateDebug - Assembles the Debug build for flavor Chocolate
assembleChocolateDebugTest - Assembles the Test build for the ChocolateDebug build
assembleChocolateMezzanine - Assembles the Mezzanine build for flavor Chocolate
assembleChocolateRelease - Assembles the Release build for flavor Chocolate
assembleDebug - Assembles all Debug builds
assembleMezzanine - Assembles all Mezzanine builds
assembleRelease - Assembles all Release builds
assembleTest - Assembles all the Test applications
assembleVanilla - Assembles all builds for flavor Vanilla
assembleVanillaDebug - Assembles the Debug build for flavor Vanilla
assembleVanillaDebugTest - Assembles the Test build for the VanillaDebug build
assembleVanillaMezzanine - Assembles the Mezzanine build for flavor Vanilla
assembleVanillaRelease - Assembles the Release build for flavor Vanilla

Install tasks
-------------
installChocolateDebug - Installs the Debug build for flavor Chocolate
installChocolateDebugTest - Installs the Test build for the ChocolateDebug build
installChocolateMezzanine - Installs the Mezzanine build for flavor Chocolate
installChocolateRelease - Installs the Release build for flavor Chocolate
installVanillaDebug - Installs the Debug build for flavor Vanilla
installVanillaDebugTest - Installs the Test build for the VanillaDebug build
installVanillaMezzanine - Installs the Mezzanine build for flavor Vanilla
installVanillaRelease - Installs the Release build for flavor Vanilla
uninstallAll - Uninstall all applications.
uninstallChocolateDebug - Uninstalls the Debug build for flavor Chocolate
uninstallChocolateDebugTest - Uninstalls the Test build for the ChocolateDebug build
uninstallChocolateMezzanine - Uninstalls the Mezzanine build for flavor Chocolate
uninstallChocolateRelease - Uninstalls the Release build for flavor Chocolate
uninstallVanillaDebug - Uninstalls the Debug build for flavor Vanilla
uninstallVanillaDebugTest - Uninstalls the Test build for the VanillaDebug build
uninstallVanillaMezzanine - Uninstalls the Mezzanine build for flavor Vanilla
uninstallVanillaRelease - Uninstalls the Release build for flavor Vanilla