Leeds signed the midfielder on loan from Juventus towards the end of the transfer window and he started in both games against Manchester United.
His level of fitness came under scrutiny in the 2-2 draw at Old Trafford last week but he was solid in the middle of the park despite the 2-0 defeat Leeds suffered at Elland Road on Sunday.
Kilgallon believes the American has got off to a good start at Leeds and he likes what the new signing has brought to the team.
He believes the midfielder has a certain presence on the pitch and is pleased to see that he does not shy away from making those tough tackles and the way he dovetails with Tyler Adams in midfield.
The former White also insisted that McKennie looked fit enough to get around the pitch as well.
Kilgallon said on BBC Radio Leeds: “He started really well, forward runs, getting behind [Patrick] Bamford, loads of energy, put a crunching tackle in.
“I like him. Great leap on him. Got a good presence in there, does a good job.
“You can see they [Adams and McKennie] are loving playing together. He knows when to sit and when to go.
“I was wondering if he would last the full 90 and how was his fitness, but no, it was all good.”
McKennie will hope to start against Everton next weekend regardless of whether Leeds get a new manager in by then.