You using flat wound strings is definitely a part of the problem, flat wounds are not exactly known for producing a lot of harmonic content and high end frequencies.
As a solution to your problem other than to swap strings to some round wounds I see 2 possible solutions, either get a good equalizer pedal or swap the pickups in your bass out with a pair that has better high frequency sensitivity.
Now I don't know what kind of pickups you got, but likely getting a good equalizer pedal will solve your problem, and also be a lot easier than swapping pickups.
As a solution to your problem other than to swap strings to some round wounds I see 2 possible solutions, either get a good equalizer pedal or swap the pickups in your bass out with a pair that has better high frequency sensitivity.
Now I don't know what kind of pickups you got, but likely getting a good equalizer pedal will solve your problem, and also be a lot easier than swapping pickups.
