[rayjay]

You will get differing opinions on this depending on what individuals have experienced themselves.
If you are going to put seahorses in this setup, I DON'T recommend using water from another tank.
Seahorses don't have a strong immune system for the most part so while some seahorses may do OK in a system set up this way, many will succumb to the pathogens introduced to them by other fish via the water transfer. Anything else transferred can also be problematic, like rock or equipment. I personally now use only complete sterile setup for a new seahorse tank.
In any case, using the old tank water itself may speed up the cycle but won't negate the need for a cycle. You can test it yourself by "challenging" the system by adding ammonia to bring the level to about 2 ppm and then see if it clears overnight to zero. If so, the tank should be cycled. Transferring live rock CAN negate the need for a cycle if enough of it, but, you are subjecting the unknowns for pathogens to your new tank.
As for the 10X thing, it means 10 times the volume of the tank.
Many years ago it was thought that seahorses needed a low flow tank, but experience over the years has shown that to be incorrect. You want enough flow to keep the detritus in suspension long enough for it to be caught up in the mechanical filtration but is not strong enough in any spot to blast the seahorses against anything that can damage them.
Normally I see a minimum of 10X recommended but in my case it's probably closer to 20X at peak and 1-15X at the least. I prefer a varied flow so some of my flow is intermittent in each tank.
For a 40g tank then, the minimum recommended flow would be 400g/hour.