Looks like you've got a solid fire deck going. The core pieces, the three fire GXs, are pretty popular in competitive decks right now, so you could use some of those deck lists as jumping off points for a deck of your own.
I believe 23 Pokemon is too many. I think you should focus on 1-2 main attackers instead of 4-5. The Chandelure line seems excessive to me; it takes up a lot of space in the deck and on your bench and doesn't provide enough utility to be worth it. I assume Salandits (GUR) are not included in your list because Ho-Oh can grab Salazzle with its GX attack, but I think you should still include 3 Salandits. Salazzle is a powerful Pokemon with a cool GX attack, and you wouldn't want to be forced to use your attack for the turn, as well as your GX attack for the game in order to get the Salazzles up. Further, I would argue that if you're running 3 Salandits, any of the GX attacks other than Ho-Oh's will do much more for you than Ho-Oh's: Tauros can act as a wall by threatening with the GX attack, Turtonator can set you up for a really strong late game, and Salazzle can turn around a sticky situation.
For trainers, restricting yourself to only S&M is a little tricky, because it means you don't have access to Professor Sycamore and N, which are by far the strongest draw Supporters in the game. The ones you should consider from S&M are Lillie (SM), Professor Kukui (SM), Hau (SM), Hala (GUR), Sophocles (BUS), and Wicke (BUS). You should probably have 8-10 of these. You could try starting with 4x Lillie, 2x Kukui, 3x Sophocles, and go from there. For other trainers, I would include 4x Ultra Ball (SM), 2x Nest Ball (SM), 2x Switch (SM), 3x Choice Band (GUR), 2x Field Blower (GUR), 3x Kiawe (BUS), 4x Guzma (BUS). That brings you up to 29 trainers, which is a pretty good amount. You can play around with things from there. Some other trainers to consider are
-Team Skull Grunt (SM), for its synergy with Gumshoos
-Altar of the Sunne (GUR), to protect your Fire types from Water type attacks
-Exp. Share (SM), to keep your Fire Energies on the board
For energies, while Tauros makes really good use of Double Colorless Energy, your Fire Pokemon basically can't use it at all. I would suggest running 13x Fire Energy only. If you really like Tauros and Gumshoos, you can run 9x Fire Energy, 4x DCE.
My suggested lists:
Keeping your favorites -
Pokemon: 16x
2x Tauros-GX (SM)
2x Pyukumuku (SM)
3x Yungoos (SM)
2x Gumshoos-GX (SM)
2x Salandit (GUR)
2x Salazzle-GX (BUS)
1x Turtonator-GX (GUR)
2x Ho-Oh-GX (BUS)
Trainers: 31x
4x Lillie (SM)
2x Professor Kukui (SM)
3x Sophocles (BUS)
4x Guzma (BUS)
3x Kiawe (BUS)
2x Team Skull Grunt (SM)
4x Ultra Ball (SM)
2x Nest Ball (SM)
2x Switch (SM)
2x Field Blower (GUR)
3x Choice Band (GUR)
Energies: 13x
9 Fire Energy
4 Double Colorless Energy
Focusing on fire -
Pokemon: 11x
3x Salandit (GUR)
3x Salazzle-GX (BUS)
2x Turtonator-GX (GUR)
3x Ho-Oh-GX (BUS)
Trainers: 36x
4x Lillie (SM)
2x Professor Kukui (SM)
4x Sophocles (BUS)
4x Guzma (BUS)
3x Kiawe (BUS)
2x Ultra Ball (SM)
4x Nest Ball (SM)
2x Switch (SM)
3x Field Blower (GUR)
1x Energy Recycler (GUR)
2x Choice Band (GUR)
2x Exp. Share (SM)
3x Altar of the Sunne (GUR)
Energies: 13x
13x Fire Energy
Hope this helps!
