The JET approval process can take anywhere from a few hours to 2 - 4 weeks or more.
If the products you sell have already been posted on JET by another seller, you could be approved almost immediately.
However, if your products are new to JET, but you have submitted a well prepared feed and your products have valid product ID(preferably an ASIN), you will probably wait about 4 weeks while the JET team is creating pages for your products.
Unfortunately, we occasionally see merchants waiting up to 4 months to be approved.
There is no guaranteed time frame, but this is what we have observed thus far.
If your products are still under review after about 2 weeks, you can contact JET support (firstname.lastname@example.org) to ask them if there is something stopping your products from being approved.