There seems to be other attributes of cup-winning teams that are more strongly correlated with success than simply drafting high. This post took a lot of time, but there’s probably still some mistakes.
You can also question the causation, but these traits are common on cup-winning teams:
-Having a starting goalie that was acquired via trade or draft, or signed with no prior NHL experience (every cup-winning team in the past 50 years)
-Having a defenseman who is top 8 or so in the world (every cup-winning team in the past 50 years except maybe Tampa in 2004 but that doesn’t count)
-Having a player who was a top 4 draft pick (29 of the past 30 cups)
-Having a coach with a career win percentage of at least 57% (21 of the past 23 cups, coaching percentage as of the beginning of this season)
-A strong penalty kill, in the top half of the league (9 of the past 10 cup winners)
-Being in the top half of the league in goals against (24 of the past 30 cup wins)
Sadly, the Flames don't have any of these attributes except a good PK (Flames are currently 6th) and Huberdeau being top 3 (edit*).
Comparatively, there are traits that have almost no correlation with winning cups:
-Only 2 of the past 10 cup winners have been ranked among the five tallest in the league.
Six of them ranked in the bottom third in height
-Weight matters much more: 5 of the past 10 winners have ranked among the 5 heaviest in the league
-Only 5 of the past 10 cup winners had one or more players who were top 10 in scoring
-The average powerplay ranking for cup winning teams in the past 10 years is only 14th