Here's what I would do, hopefully it will help,
Make sure your battery is ok, your timing is correct so the points open when they are meant to
Also make sure the points are gapped correctly.
I'm assuming the rest of your wiring loom and earths are in good order and your ignition switch is working.
Get yourself a new spark plug, yes a new one, rule this out as I've seen new plugs that are faulty.
Pull the coil lead off the plug and connect it to the new spark plug.
With the new spark plug out of the engine hold the white part of the plug against the cylinder head and crank the engine.
Make sure you turn on the ignition and you do not touch the end of the plug when you do this!
No spark? Let's check the generator then as this is easier than checking the coil due to it's location,,,,
Get yourself a bulb with two wires attached with crocodile clips at the ends.
Locate the Black ignition wire from the generator that connects to the coil, disconnect it and connect it to one of the wires from the bulb. Connect the other wire from the bulb to a good earth.
Crank the engine, if the generator is ok you should see the bulb flash intermittently.
If the bulb stays on check the points and or replace the condenser.
If you don't get anything then you need to look further at the generator.
If your bulb flashed intermittently then it looks secondary coil related, to check this you need two wires with crocodile clips on each end. Connect one wire to the negative of the battery and the other to the ground point on the coil.
Connect the other wire to the positive terminal on the battery.
Hold the spark plug to the engine and brush the end of the positive test wire against the positive terminal of the coil.
No spark, then replace the coil.
This should hopefully help you localise the problem.
There's one last bit I'd check too, but as I'm no auto electrician I'm not sure if this is the case on 6v ST70's so if someone can confirm this I'd be grateful. Check the neutral light switch on the engine, I know on another bike I owned this went faulty, as the bike thought it was not in neutral if would not start. Hopefully someone can confirm this
Good luck, Let us know how you get on,
Best,
Blue