The best place to start for any Trick Room team is deciding on a trick room user. All the possible ones are listed here. The best Trick Room user for Battle Spot is probably Slowbro/Mega-Slowbro, but you can certainly mix it up by using Pokemon like Bronzong, Diancie, Gothitelle, Beheeyem, Porygon2, Cresselia, Aromatisse, etc. It would be a good idea to use at least two Trick Room users on your team.
Remember that Battle Spot is a 4 vs 4 battle, which are selected from a full team of 6. So in any given battle you will not be bringing all of your Pokemon, but instead choosing the ones you feel has the best match-up for the opposing team. So having two Trick Room Pokemon means that you are not bringing the same Trick Room setter to every battle, but still have the choice. You can also choose to bring both Trick Room users to a battle, if you want to, so you can reset the Trick Room even if your main Trick Room setter faints.
Next, consider which Mega evolutions you may want to use. Mega Slowbro is of course of a good Pokemon for this, as it is very slow and sets up its own Trick Room. Since you can only have one Mega-Pokemon in a single battle, you might prefer to use regular Slowbro, and to bring a more offensive Mega, however. But, again, you can have two Mega-evolving Pokemon on your team, so you have that choice in which one to bring. Mega Banette also has access to Trick Room, but its Speed is high enough where it does not really benefit from using it (not to mention Prankster makes it irrelevant). I find Mega Mawile and Mega Camerupt to be especially good when used under Trick Room, although any slow Mega Evolution would work (others include Sableye, Abomasnow, and Steelix).
Finally it is time to round out the rest of the team. Which Pokemon you choose here will depend on the ones you have already chosen. It is a good idea to choose Pokemon that not only work well in Trick Room (i.e. Pokemon with a low Speed stat), but also those that are effective outside of Trick Room, for when it wears off. The best options are Pokemon that hit extremely hard, but are also hindered (under normal circumstances) by a very low Speed stat. Pokemon like Escavalier, Beeheyem, Dragalge, Marowak, Azumarill, and Conkeldurr (these are just examples, there are many others) are absolutely terrifying under Trick Room. Most of these Pokemon also tend to do fairly well when not in Trick Room, which like I said before is also an advantage. Slightly less traditional Trick Room Pokemon that do well would include Talonflame or Sableye, as their priority moves bypass Trick Room completely.
The main problem with Trick Room is that it only lasts 5 turns. Fortunately most Battle Spot battles will not last much longer than that. It does make highly defensive Pokemon less effective, however, as Trick Room will generally run out while they stall out the battle. So either Hyper Offence or (in some cases) a more balanced team will definitely use Trick Room better.
So, for a final team, consider using something along the lines of: Slowbro, Beheeyem, Mega-Mawile, Escavalier, Talonflame, and Dragalge. Note that I chose these Pokemon largely because they are some of my favourites, however there are Pokemon that may work better out there. It is all about trying it yourself and finding what works best for you. Trick Room teams can be built in many different ways, and the Pokemon I chose above focus largely on offence (except for the Slowbro, although even that can be built offensively if you want to). The important point is that there is no one way to build a Trick Room team, and all I have given is suggestions on how to go about doing it.
Note that originally I wrote this from a singles perspective, because that is what I usually play, and I didn't see the Doubles tag until I had pretty much finished. Most of the advise is still relevant to doubles, however, and I went back and changed a few things to relate it more specifically to doubles. I do have less experience with the doubles meta-game, however.
I didn't really use any, but here are a couple of pages you may find useful when building your Trick Room team. This one lists all the Pokemon that learns Trick Room.
This one lists all the stats of the final evolutions. You can sort it to list them in order of speed, which is useful for seeing the slowest fully evolved Pokemon.
