Anti Magic field does not disrupt Slow Fall.

The lead rules developer Jeremy Crawford addresses this in the Sage Advice Compendium.

Within the worlds of Dungeons and Dragons, there are two types of magic:

• the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
• the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect

Effects that cancel, dispel or nullify magic are concerned only with the second kind of magic. The first is just assumed to be part of the natural physical laws that allow a fantasy world to exist.

How to tell the difference? The Sage Advice Compendium offers a test:

1. Is it a magic item?

2. Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?

3. Is it a spell attack?

4. Is it fueled by the use of spell slots?

5. Does its description say it’s magical?

If any one of these questions can be answer "yes", then the effect, ability or item is magical for the purposes of being affected by magic cancelling effects.

None of the answers are yes. Slow fall is not cancelled by Antimagic Field.

Anti Magic field does not disrupt Slow Fall.

The lead rules developer Jeremy Crawford addresses this in the Sage Advice Compendium.

Within the worlds of Dungeons and Dragons, there are two types of magic:

• the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
• the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect

Effects that cancel, dispel or nullify magic are concerned only with the second kind of magic. The first is just assumed to be part of the natural physical laws that allow a fantasy world to exist.

Here is what Slow Fall says:

Beginning at 4th Level, you can use your Reaction when you fall to reduce any Falling damage you take by an amount equal to five times your monk level. (PHB, Monk)

How to tell if that's magical: Sage Advice Compendium offers a test.

1. Is it a magic item?

2. Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?

3. Is it a spell attack?

4. Is it fueled by the use of spell slots?

5. Does its description say it’s magical?

If any one of these questions can be answer "yes", then the effect, ability or item is magical for the purposes of being affected by magic cancelling effects.

None of the answers are yes. Slow fall is not cancelled by Antimagic Field.