If the clematis roots are very close to the base of the trees, this would have a detrimental effect on the whole plant's growth, not just the flowers.

In the wild we have seen Clematis alpina twining itself through conifers. Beautiful, no problem at all.

I have a clematis clambering over/through several conifers to no detriment that i can tell.

At Burford House Gardens Tenbury Wells, years ago when John Treasure gardened there ,I think he pioneered growing Clematis through all sorts of shrubs and conifers.