The measure you're after is what's known as the peak flow rate, measured in ml/sec. This is the best simple indication of any outflow obstruction.
The peak flow rate typically happens 4-8 seconds after the stream starts for a healthy man. A value ≥ 10ml/sec is considered acceptable for a man of our sort of age. For someone with no prostate problems, it could be 25-30ml/sec. The peak flow isn't maintained for long, as flow rate drops off as the bladder empties.
You need a peak flow rate meter to measure this. There are some other things you can measure which might be interesting, but not clinically used. Typical length of time peeing is 22 seconds, and you could measure your average flow rate by timing you peeing into a measuring jug, but I don't know what typical figures for that are.
Men pee slower at night and when they've just woken up. This is because the internal urinary sphincter is under the control of part of the autonomous nervous system which takes longer to wake up than your conscious nervous system, although any outflow obstruction might make this effect more noticeable. However, you don't want to measure your peak flow on these occasions.
One thing to check for is, are you still fully emptying your bladder? Your sphincter relaxes for a set period of time which is normally plenty enough to empty your bladder. However, if you are peeing very slowly, you won't empty your bladder in this time, known as incomplete voiding. This raises the risk of acquiring a urinary infection, because the urine left behind each time keeps any infection seeded. It will also cause you to need the toilet more often because you aren't starting with an empty bladder each time. One way to check for this is to do what's called double voiding. After you finished peeing, wait 60 seconds, and then have another pee. If there's more there than the urine your kidneys collected in that 60 seconds, then you didn't fully empty first time. You can use double voiding as a method to ensure you have fully emptied each time, as an alternative to Tamsulosin.