you could try and diy your own flow meter by using four resistors, doesn't matter if they are negative temp co or positive temp co resistors, but they need to have significant temperature coefficients that are linear. you can use four, 100 ohm platinum rtd's (they make fake platinum rtds for a few bucks or less each)
buy a digital scale. doesn't matter if its 100 grams or 100 kilograms capacity. they all use a strain gauge which has about a 2% resistance change at full load.
epoxy the four RTD resistors to the copper line you want to measure the flow rate of, in pairs, about 3 inches apart.
wire up the digital scale as if those 4 resistors were a strain gauge, in a bridge configuration.
with no oil flowing, use a pushbutton switch to short the mid point of the bridge together and turn the scale on. the scale will read zero grams. open the switch and you'll see some offset.
tweak the value of one of the resistors by adding some resistance in series with it, until the scale reads zero when you short out the bridge and turn the scale on.
now what you do is add a resistor in between those 2 pairs of resistors, and you send some current through it. maybe half a watt worth of heat. maybe it takes 1 watt of heat. epoxy say, a 10K resistor and .5 amp fuse and run it from a 120v line.
the oil flowing will cool off the first resistor and heat up the second resistor.
flow rate is proportional to the digital scale readout.
(because they all auto turn off, you'll have to press the button to short out the bridge, turn the scale on, then release the switch and the displayed value will be the oil flow rate)
to get better accuracy you will need to ensure the heater has a constant current or a constant voltage through it. you could use a cell phone charger to send 5 volts through a 25 ohm resistor, should be 1% or so accurate across normal temperature changes.