If you look at the ELOs from the game you posted, it's obvious why you lost:
3 Gold 5s vs 4 low Silvers.
Some will say "oh that's not that big of a difference". Silver 5 is basically Bronze 0.5, there is literally no difference between a Silver 5 & a bronze 1 other than they didn't get trolls in their promo series enough to lose it. lol
In every way possible, your team was outmatched where it counted. Also, Flex 5s sucks because of exactly this reason, it's almost never evenly matched.
My recommendation would be get a good duo & don't play Flex, play Solo/Duo only, and try to both get carry roles. Also, like others have said, vision wins games, so when playing support, get a vision item & red trinket.