The KnotInfo database has two parts, the collection of knot invariants and the collection of diagrams. Both can be downloaded in full. However, BE WARNED both databases are very large.
KnotInfo invariants are kept in an Excel Spreadsheet. For each invariant, there are two columns: one has the value of the invariant, the other has possible links to references. It should not be hard to isolate out the data of interest. The file is roughly 11MB : Database of knot invariants.
The diagrams in KnotInfo are all png files. The full collection can be downloaded as a tarred and zipped file which will have to be unpacked. Compressed it is 40MB. Unpacked it contains roughly 9,000 files: each knot diagram as a png file, its mirror image, and a thumbnail. Knot Diagrams.