Now first of all, regarding the specific case that motivated this question, you are right in that a flag being unhandled for a week is indeed a bit too long and might be worrying. However, the specific flag you are talking about was a close-flag. Close-flags aren't directly presented to the moderators but only enqueue the post into the close-voting review queue (accessible by any user with close-voting privileges, i.e. 3,000 reputation).
This also means that those flags aren't directly marked as helpful/declined by the moderators but are only automatically handled by the system depending on the close-reviews, as detailed in this answer. When some other user votes for closing the question for the same reason (no matter if from the queue or just the post), it will be marked "helpful" (disregarding if the question does end up closed or not). When three users (or one moderator) vote "Leave Open" from the review queue, the post will be removed from the queue and all pending closure flags will be "declined" (the existing close-votes stay, though, and the question can very well be closed afterwards).
In your case, you flagged a question for closure, but the question simply hasn't been voted to be closed for the same reason since you flagged it (there were 2 close-votes for another reason, though), neither has it been voted to be left open from the review queue, thus the flag still lingers pending until someone either votes for your reason, the question gets closed, or removed from the queue.
So much to the specific case. Now more about the general question for guidelines about when to ask about a pending flag. This isn't that easy to tell and usually depends a bit on the specific flag. If something isn't that urgent, there is no problem with a flag pending a bit. Especially close-flags, due to their above described nature, can end up pending for a little longer now and then. And flags that are more urgent (or more direct, like direct moderator attention flags) usually also get handled comparably faster.
In general, there is a very low chance that a flag even can "fall through the cracks". Direct moderator attention flags are signalled to the moderators rather clearly (and won't go away unless resolved) and will usually be handled as soon as possible, depending on their clarity. While some flags might take a bit longer to decide upon, including some moderator discussion behind the curtains, they should be resolved after maybe 3 days at maximum (often the same day, though). The site doesn't really generate many flags at all, maybe 1-2 per day on average? And even the less direct close-flags should eventually get handled some day, even if they can have to wait a bit longer as apparent from your case. Any kind of flag will usually not end up being downright forgotten, since it will always cram up some kind of queue that has to be emptied sooner or later.
So it depends a bit on personal judgment as well as how urgent you deem the specific flag and its handling. But in any case, if you have questions about a flag, be it if you're not sure you were right to flag, or just wondering if it has already been noticed or how it will be handled, feel free to ask the moderators in chat, either in our general chatroom or in a personal chatroom if you don't want to discuss matters in public. Asking can't hurt anyone and the worst response you can get is being told that the moderators can't or don't want to say anything about it, which would be rather unusual in the first place.
Searching a bit further, it actually can happen that some kinds of flags get marked as "aged away" when not being handled otherwise. It depends on the specific type of flag when this happens exactly, and the details are listed in this related question and its answers. In short
- Offensive and spam flags age away after 2 days.
- Offensive comment flags age away after 4 days.
- Close/Reopen flags again depend on the treatment of the review queue.
- Everything else doesn't age away.
So seeing a flag marked as "aged away" might be a reliable sign that it did indeed "fall through the cracks" in some way or another, which might be a reason to inquire from the moderators why this happened. But this still depends on the particular flag. For close-flags it's a sign that the community hasn't decided into any particular direction at all, which could point to a larger meta discussion about the question, the close-reason in general, or just the community's dedication to the review queue being necessary. For offensive and spam flags this should not happen and it might really be a good idea to remind the moderators of the flag in this case, since those are usually rather serious and clear-cut and need to be handled somehow (since they should be used carefully in the first place anyway). And a comment flag is, well, just a comment flag afterall and you have to decide for yourself how important you deem that (but "offensive" is still a major accusation that should be investigated by the moderators).
But all in all I've never seen a flag marked "aged away" during my entire time as an active flagger and would deem that a very rare occurence in the first place (at least on a site as small as ours).