When I hear expressions like "you need to get trained up", I think the up is, at best, superfluous and probably grammatically incorrect.
Is that the case, or does the up serve a purpose?
Up has numerous uses and, as the OED notes, ‘the variety . . . is so great that the adverb comes to present a number of highly divergent and even directly opposite senses’.
Your example is certainly grammatical. The OED’s definition in this sense is
The use of train up isn’t new. The entry gives this supporting citation from the mid-seventeenth century: