Getting your export
How long before I get the export?
That is up to Snapchat. Often a few hours to a few days, but a large archive can take longer. You get an email when it is ready.
The processing time is Snapchat's, not ours, and it varies. Often it is a matter of a few hours to a few days. If you have a very large archive it can stretch out further: they have to pack up everything you have ever saved, and that takes time.
You get an email with a download link once the export is finished. If nothing has arrived after a week it is worth checking your spam folder, and checking that the email address on the account is one you actually read. Plenty of people have an old address attached to Snapchat from their school days and have forgotten about it.
Since the waiting time is entirely outside your control, it is an argument for asking for the export early rather than waiting until it is urgent. Especially if you are over the 5 GB limit and do not know exactly when your grace period ends. You do not want to discover then that the queue is long.
One practical detail: ask for the export when you know you will have time to download it over the next few days. The link expires, and reordering means waiting in the queue all over again.
When the email arrives, download all the parts to your computer straight away. It is easier to do it in one go than to come back to it later and try to remember which files you already fetched, and the links have a habit of expiring exactly when you finally have time.