Bike isn't starting, kicking doesn't produce spark at the plugs. Also, there's very little resistance when kicking. I can hear something continue spinning after the kick as well. I pulled the clutch and it looks fine.

Battery is good, lights all work. Ignition points look ok. Haven't tested voltage at the ignition coils yet but they also look fairly new. 

The only thing I haven't tested is compression at the cylinder. Does anyone have any thoughts or ideas before I check that? If there is no compression, does anybody know how I can figure out what engines I can swap into this frame?

2 stroke twins don't have the same kind of resistance to kicking as singles, so don't necessarily compare the feeling. but do use a compression tester, 120+ PSI per cylinder is what you'll need to light it off.

But no spark must be solved. Need to determine if the ignition is powered by the battery, so look to see if 2 small primary wires come off the coils. If yes, then you must have a solid battery, and working ignition points. As you mentioned, check for battery voltage key on at the primary wires of the coils. If OK, then the points must be extremely clean, so use a points file, or very fine sandpaper to clean the contacts, AND THEN clean the contacts thoroughly after you file them (brakecleaner & compressed air, then wipe the contacts when closed with paper). They must be 100% clean, any debris will prevent grounding when the contacts are closed.

Is the crank actually turning. Put something down one plug hole just to verify that. If it is turning but not sparking it'll need a good battery to spark & "i think" they were only 6 volt on those. Also--if its Not Turning, the clutch is on the end of the crank on those so could it be burnt out--"unlikely". Could the center adjuster be adjust by someone so its already separating the plates, so its slipping while kicking & compression is just letting the clutch slip & not turn the crank, or very slowly turning it. I'm familiar with the YDS3 & this just looks a bigger version. Mind you that was about 1970 when i had one right apart haha. Unlikely to have put a hole in two pistons. Kickstart was quite high geared on those yds3's so compression should feel quite hard to kick especially as its a 305. That's all my guessing for now.

Here's a link to the parts so you can look through everything. I was guessing a bit that the kickstart drives through the clutch & not bypassing it, so relies on the clutch gripping for the kickstart to drive through to the crank. If its like that you wouldn't be able to start it in gear with clutch pulled in like more modern motors.

www.partzilla.com/catalog/yamaha/motorcycle/1966/ym1s

Thanks for all the suggestions so far. The ignition points are clean so I don't think that's the issue.

I'm going to drop some oil into the plugs like you said and see if it's turning. I'm pretty sure you're right about the kickstart being driven through the clutch. The clutch plates looked ok. I'll have to pull it apart and go a bit deeper this time to make sure it's engaging

I ran a compression test today, got absolutely nothing out of it. I had it secured all the way into the spark plug hole, and cranking the kickstarter didn't move the needle at all.

I also tried pouring a bit of oil into the spark plug hole and kicking, nothing came back out. 

So it seems the problem has to be that the kickstarter isn't engaging the crank. My question is, what is between the kickstarter and the crank, other than the clutch? I pulled out the clutch plates and they look perfectly fine, and in order. The clutch line is properly adjusted to spec. Do I need to go in from the clutch side (left) or should I start pulling apart the motor from the generator side?

The kickstarter rolls on an axle which has a spring loaded gear which comes out about 3/4" and engages the entire clutch primary gear. It should look like this: 

You may have a broken spring, either the one with the dog ear at about 6 o'clock, or the one slightly out of focus at about 9:00, or the teeth on the moving gear may be missing, enough of them to cause the failure to engage.
Drain the transmission fluid, remove the kick start lever, open the right side case cover, and see if you can find what's not right by having a look-see.

That engine is likely based on the old German design Yamaha started with... Can't think of designers name right now.  Anyway, probably quite different than the enduros we're used to... I'll see if I can find an old manual someplace.

Oil down lug holes won't hurt but i meant put a screwdriver or something down there to verify pistons are going up & down. But reading back a bit i think you've found that out. Put a spanner on the crank bolt on the ignition end & see if it turns. Be careful though as that bolt is likely quite small so don't force it too hard.

Looking at the photo of the kickstart assembly posted reminded me of the kickstart issue some of the 175's had. The piece at the end with the "ear" pointing at 11 o'clock was press fit onto the shaft, and would slip with time and use (I know this is discussed on the site elsewhere). The result was that the arm would just slip inside that piece and stepping on the start lever would not turn the clutch, thus the crank, and no start. 

This assembly looks very, very similar to those, IMHO. Given the "vintage" of the design, perhaps this is what is happening on your YM1 twin?  Maybe worth digging that bit out for a look?