Not so simple. You never mentioned whether you want a cell phone with a
plan (locked in), prepaid phone (locked in), or an unlocked phone. You
won't get a featureless phone for what you specified as your criteria.
To connect to Gmail means Internet access either via cellular data or
wi-fi connectivity along with running an app on the phone to do the sync
and local management of your contacts.
A dumb flip phone will already provide Internet access via cellular data
using a very crippled web browser with minimal features shown on the
tiny display of the flip phone. So you could use up your data minutes
connecting your cell phone to Gmail; however, that will let you see your
contacts, not dial them from your flip phone. As I recall (I never used
it), you can look at your contacts in your Google account and have
Google call that number. It asks for which phone to call you. You use
their web UI to start the call, it calls you, and then it calls the
contact's number. So, indirectly, you could use your Gmail contacts to
make calls by using the web browsing in the flip phone to connect to
your Gmail contacts. I'm pretty sure the outdated and crippled web
browser in the flip phone, slow cellular data service, and tiny screen
on the flip phone are going to make that experience suck.
Another criteria you didn't mention is price. What is your top price
that you will pay? Are you willing to wait until there is a sale on a
smartphone? I happened to grab the Samsung Galaxy Core Prime when
BestBuy had it on sale for $50 (along with a Samsung EVO 64GB microSD
card for $20). I think it was some Samsung sale for a week. Far
cheaper than anywhere else that I had looked. Also, a phone by itself
is worthless. You'll need a cellular carrier provider. Are you willing
to buy used to reduce the price? See, there are more criteria than you
mentioned when getting a phone.
I don't much use my cell phones so I get Tracfone-locked cell phones
because that service is cheap. Minutes rollover indefinitely, I never
use up all what I buy. You can get triple-minute phones where what you
buy gets tripled, so I buy the 400-minute airtime annual card which
gives me 1200 minutes per year for only $100 (they used to have an
option to pay $150 for the 400 minutes but it lasted 2 years), plus I
usually got a bonus code that added another 200 minutes. For me, 1400
minutes per year is far more than I need just for talk minutes. I don't
do Internet on dump flip phones because the web UI sucks. The phone
will be cheaper if you buy it with a service but I don't know if you
want an unlocked phone.
The problem with a flip phone is screen size. How are you going to see
the web page on such a tiny screen? How will the page appear using the
limited web browser fixed inside the flip phone (you won't get a choice
of web browser)? How fast (er, slow) is your cellular data service?
Are you willing to eat up your cellular data minutes connecting your
flip phone to the Internet to get at Gmail? You won't have use of much
faster wi-fi hotspots to use which could be free, like at home, work,
restaurant, stores, etc. You could try browsing to Gmail Contacts on
your existing cell phone to start a call from there to see if the web UI
is usable.