can slack plausibly cause ADA compliance problems re: visually impaired people? or would it end up as "use the browser client with a screen reader and be glad you can do that"
The ADA only applies to certain types of "public" private businesses. Like grocery stores and bakeries, hotels, etc. I have never heard of it applying to any private software (that isn't government related). You can always use some other chat software or none at all.
However, I would imagine that as a company, if you require employees to use specific software as a condition of employment and no accommodation can be made, you might run into trouble as an employer.