Im trying to play some rock songs that are finger picked and Im having issues with solos. The main problem is playing notes on the same string, they dont really "flow" one into another, it sounds more staccato like because the finger sort of mutes the string before the string is plucked.

Any tips to overcome this issue? Do I have to hit the string harder or maybe a quicker motion?

The classical method is likely the best, some of the folks using this technique can display amazing speed and smoothness.
However, it does take a long time to master for most people.
Another method is to alternate thumb and another finger...I use the ring finger. This is the method that Chet Atkins used.... But he admitted the classical method was likely better.