Flush, but engine temp. gauge is not working!!

[CEE1NG_RED]

Ok. I finally had fixed my transmission leak (crosses finger), but while warming up the '67 truck, the lower rad. hose started leaking/spraying old coolant (which needed to be replaced anyways since it was brownish in color). So I turned off the car and let the hot coolant/pressure leak out.

Anyways, I had changed the lower and upper hoses the day after, and found out that the truck did not come with a thermostat!!! So, I bought a 160* stat from NAPA and now comes to flushing the gunk and brown fluid from the system. Question is, is it safe to do myself as the temp. gauage is not working? What is the process of flushing a system the right way (esp. if my gauge is not working)?? The coolant from the radiator is already flushed out, just need to do the whole system flush.

LMK what step by step do I need to take. Thank you...