Will this comp cams kit require machine work?

If you have a stock '70 318, you dont have Magnum based heads. you have LA 318 heads. Are you certain you have Magnum heads? That cam will work, as will the lifters, but you will need to address the spring issue and make sure the pushrods are the type that have oil passages if you do indeed have Magnums.

Rustydusty is the one that said he has magnum heads. Not the OP.