No, flywheel does not need to be replaced. If you used a 6V starter, same as came off of it, you are OK. If it's a 235 from the 12V era and used a 12V starter, same as came off it, it's also OK. Kevin is saying you can't mix them unless flywheel matches starter. (teeth/pitch)
Provided you have the correct starter, it seems like a wiring issue as you said. If you advise if you have a foot start or somehow have a solenoid starter instead, I will go over the wiring with you.
I understand you just want to wire enough to get it started. No problem. Make sure you are VERY specific with wiring. You did not explain how you have it wired. EVERY wire, every cable, every ground. Just saying you have + connected to ballast and neg to dizzy doesn't get it. There are certainly more wires than that? We can't catch a miswire until we know how you have it wired.
See you tomorrow.