Thanks for posting a picture.
The seedling is still too small to confirm it's a fly trap. Like many seeds, fly traps put out two cotyledons ("seed leaves") first. The next leaf should look like a tiny trap.
Either way, keep growing it under "summer" conditions. It needs much more time to establish leaves and roots.
ALGAE
There is green sludge on the surface of the pot. That's algae, which can develop when there's not enough air circulation around the pot and too much water.
Recommendation: Find a pot that's at least 15 cm tall. It doesn't have to be wide. Fly traps at this age need space to grow long roots, but the leaf part of the plant will stay compact.
You can repot this seedling now into that better container. Here's how:
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Read up on best potting media. If whatever you got in your kit is a peat/sand/perlite mix and you have some left over, you can use that. Many people recommend rinsing your potting mixture several times with distilled or rain water. I pour rain water into a bowl with my peat mix, squeeze water through, rinse, repeat. This helps remove mold and algae spores. Some people microwave their peat mix.
— Use a spoon to carefully dig out a deep plug of peat containing your seedling, disturbing the roots as little as possible. If you scoop a big enough chunk, it'll be fine. Transplant that plug into your prepared new pot. Scrape off any visible algae (or do this before scooping).
I'm use nice tall-ish yogurt containers with the labels removed, and holes punched in the bottom. Make sure the pot can drain. Plan to water from the bottom — with seedlings this small, watering from the top can push the seedling around and hassle the roots. So set your pot in some kind of dish that you can pour water into. Let the pot soak up as much water as it can, then discard the excess.
Get rid of the clear plastic tube. That's preventing air circulation. Fly traps don't require moist humid air. If you need to protect your seedling from a cat or similar, hang your whole pot/saucer rig out of reach.
Use only distilled water, reverse osmosis water, or rain water. I boil my rain water to kill off algae, mold, other seeds.