Roses may be in flower then if the weather is good, but peonies will be very unlikely to flower in their first season and you would be better trying to find someone who has some already.

Put "flowering June" into Google for lots of suggestions. You can see any you fancy by putting them into google images.

The snag is you want the plants to flower for a specific day in June, this isn't as easy as you think it might be. Yes roses flower in June but will the blooms be good on the day you actually need them? The reason florists charge so much for flowers is that they have to guarantee to supply what you want on a specific day. Many cottage garden type flowers do not hold up well when cut and you will need to consider the colours you want too.

Yes, as MG says it is whether they would be fit for the day. It is a lovely idea and I would go for it, but have a back up strategy. Unless you are the kind of folk that would enjoy the the hit and miss approach to things...Could be fun laughing at Uncle Al's attempt, and being astounded by Aunt Mary's (cheating) expertise.