Can I put rooted clones directly into flowering?

Yes, you can do it, but they won't yield much unless they've at least
formed an adequate root system before you flower them.

First of all, the term "rooted clone" is pretty misleading in the context of the stories
you read about doing sog grows.

The term "rooted clone" to most people is exactly what it sounds like...
a clone that has just formed its roots.

The point about going straight into budding, usually is speaking about the fact that proper clones are already "dna age mature", thus ready to go to budding as soon as you wish.

But reading between the lines, you're still going to need to veg the clone some to allow it to develop a more adequate root system.

In the context of sog grows, the idea of going to bud as a small clone, is related to the idea of packing more plants per square foot, and sometimes (with the right strain) for the purpose of doing a single spike type "budsickle" sog grow, also often used in some perpetual harvest methods.

Even for the spike type grow, if you desire a rack full of budsickles to look like small tree trunks, or donkey dicks (as they say), you must veg the clone at least a week in hydro, two or three weeks in soil. The longer the better.

In any style, going into flowering, your yield is directly related to the amount of rooting the clone has done during vegetative growth, and also the amount of vegetative growth to support more yield.

Now don't get me wrong here, roots will continue to grow after the clone is in budding,
but in order to get a good start in budding, the clone must have a sufficiently developed root system BEFORE it goes to budding.

Bigger roots before flowering will always give you bigger and better buds.