Is there an option for "get SMS delivery reports"? Possibly under settings/text msg. I'm assuming you are not referring to chat, since that indicator is discreet.
When I was using the default samsung messages app, a blue dot would indicate that the contact also had Verizon's enhanced messaging enabled. Not sure if this is what you are describing.
The settings look correct. When you click on contacts in the messages app, do you see a little blue dot next to the contact that you are trying to chat with? That blue dot denotes chat enabled.