I don't think that Titanium welding rod is available flux coated and, even then, you would probably have to buy a half pound or more. 1/16" Grade 2 Titanium rod is available by the foot at McMaster-Carr Supply.https://www.mcmaster.com/#titanium/=1632hnn
A two foot piece is $3.05, but you would probably have to pad the order out to keep from getting killed on shipping. Grade 2 Titanium is soft and can be bent. Grade 5 is harder, but isn't available in 1/16" dia. I've used 1/16" Stainless steel TIG welding rod to make little skewers and stakes before. It's heavier than Titanium, but easier to find. If you know of a welding shop somewhere, they might have some stainless TIG rod. I doubt that you will find many shops that weld Titanium unless you are in an area that has aerospace industries. I find McMaster to be a handy source for small quantities of difficult to find materials like Stainless Welded Wire Mesh:https://www.mcmaster.com/#stainless-steel-mesh/=1632m8t
I have used the 2 X 2 mesh to make a pot support for an alcohol stove. It can be cut with tin snips and rolled into a cylinder.