Can I use an aluminium heatsink in a inox chimney?
Most metal stacks are only rated for 5-600 degrees. Yes you can get them glowing red but we used to provide a magnet that had a temp gauge on it when we installed wood stoves. 

I have seen fins added to the pipes but would urge caution if you make a cool spot on the pipe creosote will build up in that location, in the 70's we tried all kinds of things that did provide extra heat to the house, I know of 1 house that had copper tubing around the stack on the single wall section, where the copper was in contact the creosote built up in less than a year. Because of the spiral it created a "turbo torch" like fire that melted the stack and really smoke damaged a large section of the home including destroying the family room. 

Back then we used a lot of "steam" bladders in the fire box, these were great for heating if the proper safeties were in place but required the plumbing to enter and exit the fire box usually through the refractory cement bottom. We put quite a few in to heat hot tubs back then but wood heat is not as popular so you don't see much of this today. 

Use caution and know that the stack, if over heated, can melt aluminum, tin, etc, You may get more heat but watch out for creosote buildup.