First, I'm not a teacher. But I'll try to help.
Your slogan (Yes, I would use 'slogan' instead of 'key phrase.') is not obscene in any way.
'Blooms with loving strokes to many years to come.'
'Blossom with loving strokes for many years to come' might work better.
The main problem that interferes with my understanding is the bolded 'to'.
Changing it to a 'for' would best convey your intended meaning.
Student or Learner