The indoors portion of the pipe to the stove, I assume, is single wall that doesn't lock together. If so, I suggest adding a few screws to hold them together.
Throughout a lifetime of wood burning, I've had about 5 backfires. Lets say you left the draft open too far for too long and you get the stove really hot. If you then shut it down too fast (setting draft to normal or closing ash drawer), the wood is still hot enough to break down at the same rate it was before, but now with limited oxygen. This causes incomplete combustion and carbon monoxide buildup and creates an explosion hazard. As the starved mixture cools, it will draw fresh air down the chimney and mix with the carbon monoxide, and when the ratio is right, BOOM! If you don't have your pipes screwed together, you'll get a house full of smoke and embers when they fly apart. You'll have a raging fire and no chimney connected. I've never gotten sick from carbon monoxide leaking out of the stove, but it will definitely cause a backfire under the right conditions.
There might be a small issue with your modified pipe. I see an air gap at the bottom of the outer layer where the sizes don't match. You might want to seal this up somehow. The top is the coldest part and will therefore condense the most creosote. An air gap will accelerate this by not allowing the top section to stay warm. The brush might have a hard time cleaning this section if not cleaned regularly.
When you do sweep your chimney, that black creosote crap is cancerous, so try not to breathe it in.
