What part of the world are you in, when you say 'small garden', how small, and where do you need the privacy - high up or just from neighbours below 25 feet? In sun or shade?

Yes, your local climate makes a big difference in the available choices, Gelda. I would use a Mulga (Acacia aneura), since I garden in the desert, but that would be pretty unusable for Bamboo, in London.

I can't think of any tree happy in the UK that does all that. I think you have to choose between evergreen and flowers, unless a shrub would do in which case a rhododendron or camellia would hit the spot, but both grow slowly and rhodos need acid soil and not all varieties get tall. Viburnum tinus grows fairly fast but again is a shrub and the flowers are not showy and appear in winter. Perhaps a variegated female holly would suit you as it does have bright berries if there's a male nearby.

Had you thought of adding trellis above your boundary and growing a climber up it?

I'd go for a Camelia as they are evergreen and have super flowers. You can also keep them in check with pruning if you don't want it to get too big.

Well there is one tree that fits the bill that's evergreen - but it's really only viable in warm, sheltered parts of the UK

Gelda, you really do need to answer Bamboo's question to get the best advice. Whether your soil is acid or alkaline will also affect the outcome.

You could try Malus Transitoria, a crab apple that profuse spring blossom and has tiny fruits in autumn. Also Cornus Kousa is a lovely tree. This has pretty white bracts in spring and fruits in the autumn. Neither tree is evergreen though and neither grows too large. I'm toying with one or other for my small garden but haven't made a decision yet.