I haven't personally done this method, but lots of videos online about doing it. I have added tallow to an injection brine before with great results, just haven't done straight tallow. I wouldn't inject "hot' tallow. I would heat it to liquify it and let it sit on the counter to come to room temperature. After injecting, I think leaving it in the fridge over night to solidify the tallow would help in slowing it's release into the muscles while cooking it.
Here's Smokin' Joe BBQ doing a choice grade brisket with Wagyu tallow
There has been some good advice provided above, but starting with a prime brisket would definitely help your odds of a better result. You are cooking the leanest part of the brisket with the flat, so give yourself a better chance by selecting the best grade you can afford.