They don't work well in series, I've tried it.

If you have 9-12VDC, one of the $1 step-down converter modules from eBay is just the ticket to power all of them,  This will convert your 12V DC to any regulated voltage you like that's lower than 12 volts.  It's also very efficient, so you don't need a high current 12V supply.  If you want 1A out for 50 parallel LED's each drawing 20ma, you'd only need 300-400ma of 12V supply to feed them using this supply.

I'd put a 100 ohm resistor in series with each of the flickering LED's to equalize the currents and adjust this for around 4-5 volts (max 5V).

You can get them in quantity for about $1/ea as well, handy to keep around.

DC-DC Buck Converter Step Down Module LM2596

If I knock the DC down to 1.5, and wire like in the attached photo, do I need resisters or rectifiers?

In all reality, this will not be illuminated very much, I would say <20 hour per year. Would a small battery pack be a thought? I am not building this for a regular layout, this is mainly a prop to be used for education. We have groups that come through our Historical Society, and I teach on local industry. This building, where they made clay tiles & block seems to be very interesting to folks. It operated from 1919-1924. I figure, if a picture is worth 1000 words, a scale model should really make an impression! Of course, we will use this scale model of the Bloomfield Clay Products Company on our seasonal layout, but in this case, it is not the main purpose.

The flickering LED's run on 3V nominal voltage.  Also, when you have a bunch in parallel, you need equalizing resistors or you risk some being different intensity, and in extreme cases, not lighting at all.  I use the 100 ohm to drop two volts at 20ma, and add the three volts and the output of the supply should be roughly 5V.  You can use a 5V cell phone charger and dispense with the extra supply, they're normally well regulated and would have plenty of power for this application.

Check the battery.  Like GRJ says, these usually run at 3V (not 1.5V). Many store-bought tealights use the CR2032 3V coin battery.

A typical CR2032 battery is rated at ~200 ma-Hrs.  A typical flickering tealight runs for about 50 hours (if you believe the package).  So a pair of AA Alkaline batteries (2 x 1.5V = 3V) which are rated at ~2000 mA-Hrs should run your 20 LEDs for 20 hours.  If this is the only electrics running on a display, it's nice not to worry about locating this near an electrical outlet, running cords that people can trip on, etc. etc.  Then change batteries once a year.