To reckon ( there is only one way to spell it) is not slang. It means to calculate or to estimate.
You can think with your brain, but you can reckon with you brain, or a calculator, or a pen and paper.
This means that yes, you can use reckon in most cases where you might say think.
Side note: to those giving out advice in these forums, if it's a word you don't use, then consult a dictionary before telling someone else your wrong opinion.