But there is no evidence.

What cannot be denied is that an unpleasant taint of speculation and financial adventurership hung at one time about the whole connection, and that the adventures invariably came to an unlucky end.
Whether Edmund Burke and William Burke were relations or not, and if so, in what degree they were relations, neither of them ever knew; they believed that their fathers sometimes called one another cousins, and that was all that they had to say on the subject.

But they were as intimate as brothers, and when William Burke went to mend his broken fortunes in India, Edmund Burke commended him to Philip Francis--then fighting his deadly duel of five years with Warren Hastings at Calcutta--as one whom he had tenderly loved, highly valued, and continually lived with in an union not to be expressed, quite since their boyish years.

"Looking back to the course of my life," he wrote in 1771, "I remember no one considerable benefit in the whole of it which I did not, mediately or immediately, derive from William Burke." There is nothing intrinsically incredible, therefore, considering this intimacy and the community of purse and home which subsisted among the three Burkes, in the theory that when Edmund Burke bought his property in Buckinghamshire, he looked for help from the speculations of Richard and William.

However this may have been, from them no help came.