I have been all over the web, and forums, and can't seem to find a definitive answer to this question...

I have been growing a Brazilian Flame Tree from seed (indoors) for a few months. I got it as part of a kit.

The kit came with a very small pot, and some peat mixture to plant the seed in, and I have been growing it in that pot.

I am not sure when I should repot it to a different pot.

Some say "after the first year", some say "when it is a few inches high", some say "when it lignifies", etc.

I am attaching a couple pics.

Any thoughts?

Repotting in bonsai includes root work. That is not urgent and can be done later.

Your tree surelly benefits from uppotting. That is putting it into a bigger pot and fill up with soil around it.

That tree needs an enormous amount of space for the roots to grow properly, and give you some decent growth speed.
And you'll need time, because that has a huge leaf, I think a trunk for it should have at least ~8cm thick to have some proportion.

I have some spececiments here with the same age and completely different sizes, on smaller pots (2~4L) 20~30cm tall around 1,5cm thick and on the ground and wooden boxes around 1,70m tall, around 5cm thick, they're around 1,5years...

This species respont very well (and must be done actually) to the taproot pruning short on the right moment (as the spring buds beggins to swell), if you plant on top of a plank or slate, this species gives you an awesome Nebari, (their roots are very destructive for sidewalks, it has a good thickening power, at least here), It's not a Brazilian species by the way, it's native from Madagascar, but they're everywhere here in Brazil. =]

Have in mind that I can have it on the ground because my climate allows, if your doesn't you'll need a big pot so you can move it under a porch on winter, they're deciduous, I have some 100% leafless already here, so be aware of that.

As they're deciduous, the best time to repot is when they just awaking from dormancy.

This species needs to be big to make a credible bonsai.
Yes, they´re all around here in Brazil, but also in Florida and some other tropical places.
If it were mine, (as already said above), I would repot it now - as tropicals can e repotted in the summer - in a much bigger container.
Of course here it is kept outdoors all year.