Like tattoos*, those heavy vests made from cotton were kind of goodluck charms. While some vests only had insignas of their firebrigades, hikeshi/firefighters often chose to have bold lining designs depicting famous heroes and auspicious scenes to boost up their moral - firefighting was an extremely dangerous job in Edo. While not on service, they would wear their vest reversed to show off the lining (and probably brag).
*Many firemen were inked! Tattoo was in fact part of their “manly/chilvalrous” persona, which would be later somehow reclaimed by modern Yakuza. We have proof of this in ukiyo-e depicting Kabuki actor playing firemen’s roles:
