Place the tofu in a tofu press for 20 minutes. Drain excess tofu. Cut into cubes.
Prepare the brown rice according to the package directions.
While the tofu is in the press, whisk together the tamari or soy sauce, rice vinegar, agave or maple syrup, grated ginger, minced garlic, and sriracha in a large bowl. Dice the vegetables, and shred the carrot and cabbage.
Add the cubed tofu to the marinade and toss to coat. Let it marinate for at least 10 minutes.
Assemble the bowls by dividing the cooked brown rice into four bowls. Add the marinated tofu, cubed avocado, cucumber, shredded carrots, and thinly sliced red cabbage.
Top with sliced green onions and chopped cilantro.
Drizzle each bowl with any of the remaining marinade in the bowl, and sprinkle with furikake flakes. Serve the vegan poke bowls with a lime wedge on the side for squeezing over the top.