I am planning to relocate the washing machine and want to drain it directly out the wall to a 4" pipe that takes the rain gutter water to a 1200 gallon holding tank. Do I still need a "trap" and vent? Any suggestions would be helpful. Thanks.

No trap or vent needed for this but it may not be a great idea. Laundry detergent and suds will not be healthy to your lawn or garden, it's a petroleum product and will kill most vegetation. Also, depending in where you live it is likely againist the plimbing code

This may be illegal depending on your local but, if you use a "safe bio degradable detergent" making
Sure you use as little as possible per load so as not to pump raw detergent out to your plants mixing
With rain water and do not add borax or bleach it should be safe. Just keep an eye out for yellowing
Foliage or any change in your plants health.