You should be able to use any soft bristle paint brush to blend the paint when it's still wet.
Chalk paint does go a streaky especially the first coat. You can wait for the paint to dry and sand it down lightly with a fine grit sandpaper before you add a second coat. If you keeping brushing chalk paint after you lay the paint down it willget streakier. Chalk paint is meant to be applied in one long stroke without going back and forth with your brush. Sometimes that is the problem. The more coats of chalk paint that you apply the less steaky it will look. sanding in between coats will help give you a smoother finish before you apply a finish coat of either wax or poly. SOme chalk paints are "chalkier" than others so you will get a a lot of dust as you sand. Annie Sloan is an example--this particular paint sands down nicely to a smoother finish. Just make sure you wipe off all the dust with a damp rag before you add a second coat of paint.
Use a mist bottle to get out any brush marks. :)
To prevent brush strokes, its also important to sand lightly with 220 grit sandpaper in between coats. This will smooth out brush strokes!