Not ideal doing first SMD ever on flex PCB. But it is not so hard. Use lot (really lot) of flux, very little solder, big iron tip (not too hot, clean). Just gently touch edge of the pins and wait 2s, solder will flow all the way down. No scrubbing or moving of the tip over pins is needed.
Do test all connections before installing in Atari. I had to rework it few times, till all the pins were connected on both sides.