i have api quickstart, bottled bacteria.... no prime though, slipped my mind buying everything else....
The 55 gallon will greatly reduce how fast the ammonia rises. I would use 100% new water with the same percentage of salt in the 13 gallon, so if you had it at 2 tablespoons per 5 gallons, due the same for the 55g. Bring the temperature of the 55g to the same value, and then raise it to 82F.
When your ammonia hits 0.5ppm or nitrites hit 0.5ppm, then you need to do a 50% water change. Test the ammonia once a day. Seachem Prime will only detoxify 1ppm of ammonia for 24-48 hours, turning it to ammonium. The test reads total ammonia, so it won't look like the ammonia has gone done. Only bacteria and water changes will bring the ammonia down.
I would get some bio-media from your brothers other tank to help seed your filter. It needs to be submerged in tank water during transportation. If your 55g tank has reached 3 tablespoons of salt per 5 gallons, then salt will help kill the ich that may reside in the media.
You can use the bottled bacteria if you want to, and see if it helps will the cycle.
Since you got the large tank, doing large water changes can be daunting. You can get a water changer that connects up to the sink, and will help with draining the water out, and refilling. I prefer to drain the water out to the garden.