I was cleaning my bike and noticed a 4mm gap between the shell and the flange. Is this normal or should I take it to the shop?

What's your inner you tells you??

take it in before its too late or it is already too late

It is possible to run normal cartridge bb's as if they were chainline-adjustable, simply ignoring the flange.

Why this bb needed such a rightward offset is unknown to me, but looks like it might be a case of a triple crank being fitted onto the the bike's former double-length bb.

I had an opposite situation, while tightening a Shimano UN7X bb into the right end of the bb shell, the flange broke completely off.
Enough of the spline remained to allow me to still turn the cup, with final tightening being done with the left-side cup as usual.

I suspect that there is sufficient engagement between the threaded cup and shell here, so as long as the cups are tight should be ok.
It would have been better if a spacer filled the gap though, which would stabilize the heavily-loaded driveside end of the bb cartridge in the shell, but Phil Wood bb's and Campagnolo's best cartridge bb's from the previous era did just fine with the two ends of the bb cartridge simply tightened against each other.

Italian thread?

Take it in or remove the crank and tighten the BB cups yourself. It's likely that it was installed properly but has loosened off over time. That is not normal.

No, it should not look like that. The next question should be does the crank move up and down and side to side (it should be wiggling all over the place). If so, somehow the BB fixed cup got unfixed and unscrewed. This is more probable with an Italian BB because the threads are not reversed (and tend to place pressure on the cup to unscrew) but I guess under the righ circumstances it could happen to any BB. I'm guessing you don't have the knowledge or tool to remove the crank arms, the BB should be removed and checked out. If there is no major scoring or pitting than it can be clean re-greased and re-installed. If you don't want to mess with it, just have your local bike shop replace the old BB with a new $25 sealed unit; should cost you about $30-40..

Thanks for the replies. I took some measurements and concluded it was done to maintain the chainline. I'll most likely buy a bb tool and some spacers to fill the gap.

Does the crank feel loose? If it is for the chainline than an unscrewed cup, the left side would have to be screwed about 10mm into the shell with no locknut. Rather than getting spacers, why not get the right size spindle?

Well, how did this work out?