Run flake8 on Python 3.

tox.ini

@@ -6,18 +6,18 @@
 # Map Python versions in GitHub Actions to tox environments to run.
 [gh-actions]
 python =
-    2.7: py27-coverage,codechecks
+    2.7: py27-coverage,codechecks2
     3.6: py36-coverage
     3.7: py37-coverage
     3.8: py38-coverage
-    3.9: py39-coverage,typechecks
+    3.9: py39-coverage,typechecks,codechecks3
     pypy-3.7: pypy3
 
 [pytest]
 twisted = 1
 
 [tox]
-envlist = typechecks,codechecks,py{27,36,37,38,39}-{coverage},pypy27,pypy3
+envlist = typechecks,codechecks2,codechecks3,py{27,36,37,38,39}-{coverage},pypy27,pypy3
 minversion = 2.4
 
 [testenv]
@@ -97,7 +97,7 @@ commands =
          coverage report
 
 
-[testenv:codechecks]
+[testenv:codechecks2]
 basepython = python2.7
 # On macOS, git inside of towncrier needs $HOME.
 passenv = HOME
@@ -128,6 +128,16 @@ commands =
          python -m towncrier.check --config towncrier.pyproject.toml
 
 
+[testenv:codechecks3]
+basepython = python3
+setenv =
+	 # If no positional arguments are given, try to run the checks on the
+	 # entire codebase, including various pieces of supporting code.
+	 DEFAULT_FILES=src integration static misc setup.py
+commands =
+         flake8 {posargs:{env:DEFAULT_FILES}}
+
+
 [testenv:typechecks]
 basepython = python3
 skip_install = True