Chimney Leaking?

I have a SS chimney. It the Selkirk stuff that Menard's sells. I think, but don't know, that it is leaking at one of the joints. It's an out and up installation that goes (bottom to top):

"T"
3-footer
3-footer
3-footer
1-footer
cap

I think it is leaking between the last two three footers. The reason I think this is because I'm getting very little creosote in the stove pipe nor in the chimney up to that joint. After that joint I'm getting pretty heavy shiny build-up. I think it's drawing some air and cooling things down too much.

I've tried re-seating the two joints but they feel tight.

Normally I would run a bead of silicon around the outside of the joint, but that joint lies within my roof flashing and I can't get to it.

Any ideas?

I guess I could disconnect between the second and third joint and lift the suspect joint out of the flashing to silicon it then drop it back down. Don't know if I have enough grunt to lift it.