Go on eBay and search 'burl veneer'. You'll get lots of hits.
Thicker veneer gives you more chance to get things flat enough and sand-able. Typical thickness these days is 1/42": pretty awful for an amateur! 1/32" is the old standard. 1/16" is rare and rather like working with lumber. Burl is a little tougher to work with as an amateur, but certainly doable. Contact cement is pretty easy; thermoplastic glues are traditional but requiring skill and tools (hot glue, hide glue, etc.). Hard setting, thermosetting, glues require good clamping; it's hard to get ripply stuff down on the substrate and get it flat enough to sand w/o fear of sanding through. I've been successful with Olive, Oak, and Walnut burl.
If you're lucky, perhaps you can buy burl solids rather than veneers. I was able to 'resaw' thick Walnut crotch into 1/2" thick planks which were stable enough for a cabinet door panel and drawer front.
If you like the look, stick with real wood veneers. I would eschew using PLam in fake wood patterns, it's true that the good ones are good from a distance.