Suggest take plug caps off and see what sparks come off bared ends of leads, held about 1/4inch from head. Should be very healthy ones at kickstart speeds. If so, then maybe the plugs are a problem (try swapping for others first of all maybe?); if no better then maybe the leads aren't well-connected to the pick-ups or the plug caps or both. Am assuming pick-ups and brushes are decent quality and in good nick.
If all seems good, next port of call has to be the contact breaker.
If you have a meter that measures capacitance, then undo the centre screw (or take the unit right off), hold the points open with a bit of insulated something, and you should see (+/-10%) 150nF (0.15 micro-Farad) across the points on the capacitance scale. With them shut, you should see, on the resistance scale, 0 ohms or as near as dammit if they are properly clean. No capacitance open, or high resistance closed are both bad.
If there's a short across the capacitor, you'll see zero capacitance but you would probably see a steady resistance reading with the points open - that shouldn't be there.
If it's one of the later type steel contact breakers, make sure the little screw that holds the cb blade spring to the bent metal mount isn't too long, and touching the capacitor. It mustn't be too long. The circuit board isn't thick - an overlong screw would be wide enough to touch both plated sides of it and short it.
Check also, if it's the steel cb unit, that the spring blade isn't kissing the camring as it goes round. If it does, you'll have problems because on them the blade is 'live'. On brass ones, the old style, it's the earth side, so a kiss won't stop the thing working.
Has to be something relatively simple I think, but only by doing one thing at a time methodically will the fault reveal itself.