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If you would like to send your condolences to family and friends of a Church official that has passed away, the Church of Jesus Christ of Latter-day Saints maintains an email address specifically for that purpose. The email, condolences@ldschurch.org, has existed at least since 2004.
In previous times, members were asked to mail their expressions of sympathy to Church headquarters. However, with the growth of technology (and the Church), today's announcement of Elder Perry's funeral arrangements didn't include that option. Instead, the Church asked that members post messages to Elder Perry's Facebook page, a request we can expect to see continued in the future for those Church officials that have formal social media accounts.
If you want to do more than send a message, a common request of the families of Church figures is to have interested parties donate to specific Church or non-profit organizations in lieu of sending flowers. Check Mormon Newsroom for information about what the specific official has requested.
Elder Perry's family has asked for donations to the Church’s Missionary or Humanitarian Fund be sent in lieu of flowers.