ok, if it's dynamic, it a pain, but doable. so much of it depends on the page that is presented with the listof files, because you have to extract them all out.

i've done it like this:

In my case, i was downloading csv files.

I've used a script task to read a web page into a string.

i then parse the string with a regular expression to get all the a href="somefile" links.

i personally had to tweak the links because they were all relative, and i needed absolute:

ie the link said <a href="Invoice_2015_10_01.csv">Invoice_2015_10_01.csv</a>

but i needed the full path of http://website.com/Subdirectory/Invoice_2015_10_01.csv

that list went into a datatable, that i passed to the next script task; it could have been a delimited string, or a string array or a list of string, but that's just the way i did it.

the next item was a script task that downloaded each file in the datatable.