On a 1967 with a generator (and a voltage regulator) if it is not charging, the "charge" idiot light should come on.
Check your battery connections both at the battery and in the engine bay - clean and tight, including the engine ground strap.

Using a voltmeter, check the battery voltage, engine off. It should be between 12V and 13.2V, lower if it is discharged. However, it may read 12V but have a bad cell and not be capable of providing the amps to crank an engine. (A fully charged lead acid battery produces 2.2V per cell and has 6 cells = 13.2V)

Using a voltmeter with the engine running, measure the voltage between the battery terminal at the solenoid and a good ground point on the engine block. With the engine at idle you should get somewhere around 14V - it needs to be higher than the battery voltage to "push" the charge back in. Raise the idle a bit and you should get a solid 14V (approx.)

If your car starts OK with a boost and runs, I'd suspect a bad battery first. Try replacing it with a good battery and go for a run. If the battery gets drained, something is wrong with the charging system. If that battery recharges, it's your battery.

To have it properly tested, it needs to be charged overnight, with low amperage around 1.5 amps or it will just show as dead, which is fine if you sell batteries.

With batteries stupicly expensive now, you can by your own chrome toaster style load tester for about $40.00

so I’ll jumpstart the car and then drive it around for a bit and I turn it off and on and the battery just dies. I’ll take to autozone see if they can test it for me. Thanks 

What is the car doing that makes you question the battery?

You can always take your car to the parts store and ask them to check the charging system.  They should be able to determine if your car has any problems... for free.

How do I know if the battery is bad vs the generator ? I have a 1967 Austin mini. The current battery is a Duralast 575cca and 710ca.