In the UI it would be nice to duplicate the selected connection, in the menu "With Selected". 

The copy would be set with the same name plus some suffix (_copy, _1, whatever) and it is useful for when you have a connection with all equal fields except something in a particular one. 
airflow/www/views.py
UserStatsChartView,
    ViewMenuModelView,
)
from flask_appbuilder.widgets import FormWidget
from flask_babel import lazy_gettext
from jinja2.utils import htmlsafe_json_dumps, pformat  
from pendulum.datetime import DateTime
from pygments import highlight, lexers
from pygments.formatters import HtmlFormatter  
from sqlalchemy import Date, and_, desc, func, or_, union_all
from sqlalchemy.orm import joinedload
from wtforms import SelectField, validators
from wtforms.validators import InputRequired
import airflow
from airflow import models, plugins_manager, settings
from airflow.api.common.experimental.mark_tasks import (
    set_dag_run_state_to_failed,
    set_dag_run_state_to_success,
)
from airflow.configuration import AIRFLOW_CONFIG, conf
from airflow.exceptions import AirflowException
from airflow.executors.executor_loader import ExecutorLoader
from airflow.jobs.base_job import BaseJob
from airflow.jobs.scheduler_job import SchedulerJob
from airflow.models import DAG, Connection, DagModel, DagTag, Log, SlaMiss, TaskFail, XCom, errors
from airflow.models.baseoperator import BaseOperator
from airflow.models.dagcode import DagCode
from airflow.models.dagrun import DagRun, DagRunType
from airflow.models.serialized_dag import SerializedDagModel
from airflow.models.taskinstance import TaskInstance