You'll find lots of posts on here about the % of flavoring. That's an important thing for taste, that % of flavoring. Percentage is of the total volume. So, yes, adding anything to an existing
juice will alter the flavor you taste because you've changed the total volume while the volume of original flavoring is unchanged so the % will change.
Since "mg" is piss-poor shorthand for mg/ml, it's pretty easy to figure out what a combination of ml's of mg/ml and ml adds up to.
If you had 10ml of 0mg/ml flavored
juice and added 5ml of 48mg/ml unflavored nicotine, you would have added 48mg/ml * 5ml = 240mg of nicotine in 10ml + 5ml = 15ml of liquid. 240mg / 15ml = 16mg/ml flavored juice.
Now if that original juice had 10% flavoring to make the taste you like in it, then after adding that imaginary 5ml of nicotine base to it, you'd have 6.7% flavoring. Some flavorings, that will be a slight drop in flavor. Some flavorings that will be a huge drop in flavor. Some flavorings will change into something so different, you will think your nicotine was highly flavored and it overpowered your original flavor. But it will change it in some way.
There's tons of posts on here as to where to get some nicotine for mixing.
ETA: If you were to buy the same juice flavor, but with nicotine, you could mix the two together and the flavor wouldn't change. (Unless they are using crappy nic, but that's a different story.) The easy math is to buy the second bottle of flavored, but with nic, juice at twice your usual nicotine level and mix it 50/50 with your original 0mg/ml juice and the result will be at your usual nicotine level.