The simplest thing you could try to do is allocate several more of the same type of object and hope one of them lands at the same memory address. For example if you can UAF a web app's user session and keep it open for a long time period (not true in the TCP bug), you might try to wait until an admin happens to log in with their session at the same address, then use their admin session.

Or you can allocate a lot of something else objects and hope a certain field overlaps, like a function pointer if you can write to it. Like suppose you can get some kind of authentication callback pointer to overlap where your packet sequence number was, maybe you can send a certain number of packets to make it point to the return instruction and skip the authentication.

At a high level, though: once you've gotten a new object allocated where the old one was, you now have two different views of the same bit of memory. You use valid operations on one view to put the other one into a corrupted state. For example: in a unixlike kernel, maybe one view has a field containing a function pointer (for method dispatch, essentially). You read that field using the other view, use it to deduce something about the target's memory layout, write a new value to the pointer, then use the field via the first view to cause execution to jump to a location you control.

For example, I remember an exploit workshop around reuse of passwd entries. The vulnerable would validate a passwd entry for a non-root user, use it a bit, and later on free and zero it out for security purposes... except it then looked at the passwd entry again in some conditions. Suddenly, the uid was non-zero at first, and zero later on, so later decisions assumed the user was root.

In a more concurrent situation, a possible vulnerability was a shared cache of these passwd entries. It wouldn't zero them out anymore, but you could create a race condition of starting requests as user A, and then hammering requests as user B, so you'd end up mixing up the permission contexts of these users. Because the passwd entry that had been released back to the pool was overwritten, and then re-read with the value from another context.

The necessary line of thinking tends to be very different from thinking about program code regularly.