DC-DC converter current limiting for charging LiFePo4 battery using SLA battery
A simple supply is not a good choice for charging liFePO4 batteries for a number of reasons.
Initially when charging LFP you supply it with current and the battery will decide what the voltage is. Practically for you this means that you need a supply that can provide a constant current to the battery. You say that you assume your supply will shut off at 20A. Assuming anything around these batteries can be a very expensive mistake and this does not give you a constant current source.
When the battery reaches the bulk voltage limit at 13.8V you need to let the battery absorb at that voltage until the current drops to C/20 (that would be 5A for a 100AH battery), and then STOP CHARGING. You can ruin your batteries by allowing them to float with a 13.8 charge voltage. Your BMS will not protect you against that.
I know links are frowned upon but there is a lot of good information on Nordkyn design's website.