pulled the plugs and laid them atop the fins so the threads were touching, kicked the bike and got a little blue-white spark on both cylinders.
no dice.
bike fired one or twice, and there seemed to be a minor backfire, she wouldn't run.
Ime, typical of any carburetted engine that has not been used for a long period, I just keep tickling and kicking, the "minor backfires" turn into longer and longer period of firing until it eventually just runs.
Btw, you are holding the throttle open a
little when you kick, are not opening the throttle as you kick?
worried that I might have timed the BB ignition to no. 2 cylinder
Not relevant on a 360 degree 4-stroke twin; BB (almost all e.i. for British twins), coil for each cylinder is connected in series to the electronics'
single switched output (Black wire on any BB), so the power to both coils' primaries is switched off when either cylinder is on its compression stroke and needs a spark; is the reason the e.i. are known as "wasted spark".
figured I'd flooded the cylinders.
Yeah ...

... I can tell that has happened when the "minor backfires" stop ... I just hold the throttle wide open, kick the engine over half a dozen or so times, let go of the throttle, tickle the carbs again, hold the throttle open a little again, start kicking again.
kick stand's ugly welding job that the broker did busted.
could not find a scratch anywhere on the bike.
The notion you can't kick start a motorcycle on the side stand is... well, idiotic. I have owned a half-dozen kick-start bikes including the 565 lb. '51 FL that have never had an issue.
This is a 53 year old Triumph, simply Meriden never at any time engineered the sidestand frame lug for the stress of the engine being kicked over. When your bike was new, iirc the US guarantee period was either three or six months, anything that broke anytime after the guarantee ended was the owner's problem.
Kicking the engine over with the bike either upright or on the centrestand (I do the latter) is hardly a chore? It is just something you either accept as part of owning an old Triumph or you strengthen the bike's sidestand lug.
BB's reference to clockwise vs. counterclockwise mean as viewed from the ignition side
Correct.
coils
Perhaps one or both is faulty
pulled the plugs and laid them atop the fins so the threads were touching, kicked the bike and got a little blue-white spark on both cylinders.
Does not sound like it? Only possibility is both plugs are not firing under compression?
One tip I received decades ago, still use when first starting an engine that has not been used for a long period, is close up the plug gaps to, say, 20 thou; after the engine starts and runs, open the gaps back out to 25 thou.
check the coils against the specs in the manual.
guessing (though I don't know) the PO had installed two 6v coils...
With the BB analogue e.i. (black Transistor Box), "6V" coils must have a primary resistance between 1.5 and 2 Ohms; less than 1.5 Ohms, too much current is drawn through the electronics, they fail prematurely; much greater than 2 Ohms (e.g. 2.2 Ohms of old PVL coils is fine), too little current is drawn, spark problems, particularly at higher rpm.
BB says:
"For low compression engines, two 12 volt coils (4 Ohm Resistance) in series are satisfactory,
Ime, while BB fitting instructions have always said that, is complete rubbish, never works, irritating nonsense.

I first dealt with Bransden Electronics long before there was internet, they offered tech advice on a dedicated phone number between 4pm and 5pm. If you phoned about an ignition problem on a twin, one of the early questions in the conversation would be whether the bike had 12V or 6V coils; if the answer was 12V, the advice would be to fit 6V, call back again if there was still a problem ...
Btw, your photo.
View attachment 59205, I never use those red insulated terminals, I have replaced too many on other people's bikes at roadsides and in campsites.

Between what BB calls the "Stator" and the Transistor Box, I use "Japanese bullets" and sockets; because both terminals have an insulator, pushed together with the terminals the insulators make an almost waterproof seal. The larger 3.9 mm (aka 4 mm) bullets/sockets are widely available but the 3.5 mm are also slightly shorter, wires do not have to be bent so sharply inside the timing cover and, if the bullets are fitted on the wires through the crankcase, those wires can be pulled out of the crankcase without cutting off the bullets.

Available from
Cycle Terminal.