Unless I still misunderstand things, if the NHL Flames have signed him to an ELC then he isn't eligible for the Heat playoffs because he wasn't on their roster on deadline day.
Different situation. There are pretty much 3 possible situations with prospects right now.
There is the "Kenny Agostino" where you sign a prospect to an ELC that starts immediately and they are ineligible for the AHL playoffs.
There is the "Brett Kulak" where you sign a prospect to an ELC that begins next season and sign them to an ATO for the remainder of the season and they are eligible for the AHL playoffs. Ryan Culkin fits in this category as well.
There is the "Morgan Klimchuk" where you have already signed the prospect earlier in their year and their contract has slid to next year and you can reassign them to the AHL and they are eligible for the AHL playoffs. Keegan Kanzig and Emile Poirier fit into this category too.
Gaudreau and Arnold could fall into either the same as Agostino or Kulak.