How do I get rid of drain flies with muriatic acid ?

Muriatic acid may or may not work. Muriatic acid is very corrosive and can cause severe skin burns. Be careful using it. In essence, you just pour it into the drain. Some people believe it is safer to pour some gel drain cleaner in the infected drain, cover the drain with plastic wrap and a cup or bowl to seal the opening. Others will pour a small amount of liquid Sevin into the drain, and seal as above.

The muriatic acid method is a chemical way to scour the soap scum and other organic matter from the interior of the drain pipes where the fly eggs hatch and the larvae feed. As Ma0641 said, it is very corrosive.

Other methods for scouring those pipes include:

Taking the drain cover off and using a brush to physically scrub out the pipes

Using an enzyme based cleaner to biologically get rid of the scum

And, again as Ma0641 said, using a gel drain cleanser.

In any case, sealing the drain while your chosen method works will keep them from breeding more flies.