Is it not possible to say "hun har mange hester" here?
Mange = many. You can own several horses without having many. So the main difference between flere and mange here is the quantity.
To me "flere" alone sounds like "flera" but in a sentence it sounds like "flere"
The answer to several= atskillinger. is that correct?
atskillige or adskillige (plural yes, but without the -r) may indeed mean several as in many or really many. But to translate several, use "flere".