Would you use a miter saw or a table saw ?

I bought the skil flooring saw and i was wondering if that could be used as well.

Any tips for not getting rought cuts ?

thickness is 1/2", width about 3 1/2"

Are you cutting to width or length? Use a table saw to cut to width. Use a miter saw to cut to length. Use a fine tooth blade for cutting to length. Use a good ripping blade for cutting to width.
What is the nosing made of? How will it be attached? Stair noses are a high stress area....make sure it is well secured.
How accurate is the skil flooring saw and what type of blade is on it?

Turn the nosing upside down and cut from the back if you are getting tear-out.

I am cutting to length actually. The Skil flooring saw has a 4-3/8 in 40 tooth carbie tipped blade. Great tool but lacking laser imo, otherwise quite accurate.
Is that fine enough ?

I've also seen people taping the area to be cut with painter's tape, is that a good practice ?

The stair nose is designed to fit with tongue and groove engineered hard wood planks. I was just going to glue that area with loctite pl construction adhesive.

Since it is kinda hard to find a matching wood filler, I'm hesitant to use finish nails on the stair nose.

If the piece is long enough make some test cuts to see if they are fine enough. When you used the skil saw to cut your flooring were the cuts fine and splinter free? If you have a miter saw with a blade with 60 or more teeth I'd use that....but don't go out and buy one for just one cut.
If you can't find matching wood filler make some using sanding dust from the same wood species and mix this with wood glue. Hide glue would be best if you are going to stain the filler.

Great idea about mixing the sanding dust with hide glue, thanks.

The skil saw were fine on the flooring, so i'll try a small piece on the nose first then.

Mix the sanding dust and glue to a consistency like peanut butter.
Also, if you can't get an exact color match make the filler darker than the board.
And, in the event the filled holes are slightly visible, space the nails in an evenly spaced, neat pattern. You could also use contrasting wood plugs, if you like that look.

If you are using a good glue to hold the nosings in place, a pin tacker that uses 18 gauge finish nails will put tiny nails into the darker part of the grain when you aim it. You should be able to find finish nails loose in the is gauge, too, but you may need to pre-drill for nailing into hard wood. You will need to set regular finish nails with a small nail set. This tiny hole almost disappears but the nail will hold the nosing in place until the glue hardens. Usually one nail on each end of the nosing does it. Wood patch for unfinished flooring, or colored putty for pre-finished flooring will finish off the job.