Valve is slowly porting games to Source 2. While TF2 hasn't been confirmed, modders are experimenting with WebAssembly (WASM) ports of the Source engine. Within 2-3 years, we may see a legitimate Team Fortress 2 Classic run at 30 FPS inside a browser tab using WebGPU.
Until then, the "No Flash" landscape is stable. Flash is dead. Long live HTML5 cloud streaming.
Less common but very effective. Boosteroid supports TF2 fully in the browser. It is a paid service, but they often have trial hours. ---- Team Fortress 2 Unblocked No Flash
If you have a decent internet connection, NVIDIA GeForce NOW is the definitive answer to "Team Fortress 2 unblocked no flash."
Why this works:
How to play:
Caveat: You must own TF2 on Steam (it’s free-to-play, so just create an account at home). Your school might block the NVIDIA domain, but most don't because it uses standard Google WebRTC protocols. Valve is slowly porting games to Source 2
If you want the TF2 feel without online restrictions: