Put the tee in the hose between heater core and radiator tank. Clamp the heater hose on the radiator side of the fill kit with a needle-nose vice-grip or specialty hose clamping tool.
Engine off. Flush water from the tee back-flows through the heater core, into the engine at the intake manifold connection, and out through the open block drains--and into the radiator via the water pump passages and lower rad hose back-flushing the radiator (assuming the thermostat is closed.) Coolant can exit the radiator at the filler neck also, but put the cap back on to back-flush the radiator via the radiator drain..
Conversely, release the clamp, re-clamp on the heater core side of the flush tee. Rad cap off to start with. Let the water run until the rad fills up. Install cap, block overflow nipple. Start the engine. Flush water goes to the "cool" tank of the radiator, into the engine via the water pump, out the block drains, and out the upper radiator hose (thermostat open or--more likely--removed) to the "hot" tank of the rad, and then out the radiator draincock.
There is some risk of running the engine low on coolant, depending on how fast it's exiting the block drains, radiator drain, and radiator filler neck.
Directing flushwater flow is a game of providing deliberate restriction here and there, installing or removing drain plugs--or opening/closing draincocks. Use the engine's water pump (engine running) to boost circulation as desired.
I try to remove the overflow bottle, add some HOT water and a little bit of detergent, and some playground sand. Slosh the sand around to "scrub" the dreck off the inside of the bottle.
It's essential to remove block drain plugs (which might be the knock sensor on some engines) so that the old coolant is thoroughly drained, and the flush water is similarly drained.
Folks have cracked blocks in the winter or at high altitude (cold weather) because they failed to remove flush water, failing to account for the trapped flush water when re-filling the cooling system with "50/50" prediluted antifreeze. What they add might be "50/50" but there's already over a gallon of straight water still in the block further diluting the coolant.
Some engines (Lookin' at you, Buick) don't have block drains. So the flush water either gets partially drained with gymnastics of lifting the rear of the vehicle, or dicking with engine core plugs, or just leaving the flush water but adding the full measure of "pure" anti-freeze before final dilution with however much water it takes to completely fill the cooling system.