Is it possible to book economy flights direct with Singapore air and use velocity points to upgrade?
No. I don’t think so. You can use Krisflyer miles to upgrade some fare types.
Note that it usually cost close to an outright award business class redemption to upgrade. So it may only be useful when say your work pays for economy and you use your Krisflyer miles to upgrade.
If you are desperate and have lots of Velocity points, there is an option to transfer Velocity points to Krisflyer miles at a ratio of 1.55:1