MMS is mostly working since a couple of years ago. You may need to enter settings which you can now do from Chatty, open “Preferences” there and then choose “SMS and MMS settings” and put the right things in the MMSC, APN and Proxy fields there. ( You may have the correct settings already by default if the right info for your provider is in the serviceproviders.xml file as mentioned here APN settings values and storage - #5 by janvlug )
The config file is at ~/.mms/modemmanager/mms in case you prefer to edit the file directly, but you should not need to do that now, I think.
One thing that is not solved yet is the case of having different APNs for mobile data and MMS, if your carrier requires that then I think you cannot get MMS and mobile data to work at the same time. But if you have the same APN for both things, which seems common, then things should work.
There is this old thread about it:
See also: