Hello Steve,
It was not just Gen. Taylor but the units of his department that used flags like this - and ones with a blue field and red St. George's cross too.
I think the earliest we can trace them to is sometime in 1863. The ones that Texas units used seem to have been made in Havana, Cuba by ex-patriot Southern women (the Trans-Miss silk supply was well-gone by this time) and sent to Texas through the blockade. Robert Maberry's excellent book on Texas flags details these.
Greg Biggs