Your team has a weakness to Water, especially Azumarill and Starmie who give this team a hard time in terms of matchups so I would suggest using a check for the two such as Ferrothorn. Ferrothorn also gives you a resistance to Dragon, Grass, Poison among other types in the metagame.
Calm Mind Clefable gives this team a rough time as well. You need a secondary wallbreaker that can handle it. Something like Kyurem-B, Bisharp or even Nidoking
Not having hazards does put your team at a disadvantage so now you really would want to run Ferrothorn or Garchomp to support Tyranitar
Chansey, Latios and Talonflame do not help this team very much.
I would suggest using a spinner over a defogger as you already have a bad matchup with the prime defog stoppers in the game. Those being Weavile and Bisharp. Starmie or Excadrill would be good here for that
Chansey doesn't do squat in terms of support. It actually hinders your team more than helping it. Sure it can switch on a few special attacks but it can't do much to retaliate and sometimes even ends up as set up fodder. Scrap it. Chansey is meant for stall based teams and the team you have here is balanced offense
Banded Talonflame doesn't work here but the Swords Dance set would so you can consider that
Overall, this team is good solely because of the Klefki/Gliscor/Tyranitar core especially because Tyranitar tears through mons after even just one Dragon Dance.
List of relevant threats to team:
Also to answer your question, in my opinion, dual screens aren't worth it especially if the opponent removes your Light Clay which would make it only last for 4-5 turns
Calm Mind Clefable gives this team a rough time as well. You need a secondary wallbreaker that can handle it. Something like Kyurem-B, Bisharp or even Nidoking
Not having hazards does put your team at a disadvantage so now you really would want to run Ferrothorn or Garchomp to support Tyranitar
Chansey, Latios and Talonflame do not help this team very much.
I would suggest using a spinner over a defogger as you already have a bad matchup with the prime defog stoppers in the game. Those being Weavile and Bisharp. Starmie or Excadrill would be good here for that
Chansey doesn't do squat in terms of support. It actually hinders your team more than helping it. Sure it can switch on a few special attacks but it can't do much to retaliate and sometimes even ends up as set up fodder. Scrap it. Chansey is meant for stall based teams and the team you have here is balanced offense
Banded Talonflame doesn't work here but the Swords Dance set would so you can consider that
Overall, this team is good solely because of the Klefki/Gliscor/Tyranitar core especially because Tyranitar tears through mons after even just one Dragon Dance.
List of relevant threats to team:
Also to answer your question, in my opinion, dual screens aren't worth it especially if the opponent removes your Light Clay which would make it only last for 4-5 turns