I have a single speed with 48/16 ratio with flip-flop wheel.
I'm considering to change fixie cog to 19t, as it is easier to skit and has more skid patches.
Will I need to enlarge my chain too?
Very likely, yes.
Your cog is 3 teeth larger, so the chain will need to be 1.5 halflinks longer which rounds to 2 half or 1 full link, OR you may be able to move your wheel forward if you have trackends instead of dropouts.
If you can't get the wheel further forward, then you will definitely require more links in the chain. Given you're changing cog its probably worth fitting a new chain anyway, and consider upgrading to 1/8" if you're using 3/32" now.
I note that 48/16 gives you exactly one skid patch, or two if you can use both legs. 48/19 will give you 19 skid patches, so that will help on tyre wear.
https://www.bikecalc.com/skid_patch_calculator is helpful for these kind of calculations.