Correct way for you would be:
if [[ $REG = 'true' && $VIN = 'true' ]]; then
    echo "$REG $VIN"
fi
This is the most correct and safe way (unlike executing your $REG and $VIN as other answers suggest). For example, what is going to happen if $REG variable is empty? Or what if it equals to something different than just true or false?
If you want boolean behavior in bash, then consider the fact that empty strings are falsy.
REG=1
if [[ $REG ]]; then
    echo '$REG is true!'
fi
or like that for multiple variables:
REG=1
VIN=''
if [[ $REG && $VIN ]]; then
    echo '$REG and $VIN are true!'
fi
if [[ $REG && ! $VIN ]]; then
    echo '$REG is true and $VIN is false!'
fi
So, if you want something to be false, then either leave it unset or use an empty string.