Compile on Fedora 21

To answer my own question: Yes. It can be easily compiled and used on Fedora.

First you have to install some dependencies:
sudo yum install glib2-devel gtk3-devel libgee-devel json-glib-devel keybinder3-devel libnotify-devel zeitgeist-devel libappindicator-gtk3-devel rest-devel vala

Then you just follow the instructions and do:
./configure
make
sudo make install

Not having an alternative for Alfred (Mac) in Linux was a giant pain in the a** :)

hi Max,

I can also confirm that compilation works in the same way for Fedora 22, with the exception of replacing yum with dnf as well as installing intltool (for which ./configure gave an error of intltool being too old). Working well so far!

You could install Synapse from russianfedora repository

su -c 'dnf install --nogpgcheck http://mirror.yandex.ru/fedora/russianfedora/russianfedora/free/fedora/russianfedora-free-release-stable.noarch.rpm http://mirror.yandex.ru/fedora/russianfedora/russianfedora/nonfree/fedora/russianfedora-nonfree-release-stable.noarch.rpm'

dnf install synapse

[root@ip201-126 ~]# dnf info synapse
Last metadata expiration check performed 0:13:27 ago on Wed Aug 12 22:04:43 2015.
Доступные пакеты
Имя : synapse
Архитектура : x86_64
Эпоха : 0
Версия : 0.2.99.1
Релиз : 1.fc22.R
Размер : 472 k
Репозиторий : russianfedora-free-updates
Краткое опи : A semantic file launcher
URL : https://launchpad.net/synapse-project
Лицензия : GPLv3+
Описание : Synapse is a semantic launcher written in Vala that you can use
            : to start applications as well as find and access relevant documents
            : and files by making use of the Zeitgeist engine.

You all could just install it from official repo again:

https://bugzilla.redhat.com/show_bug.cgi?id=1256097

synapse-0.2.99.2-1.fc23 http://koji.russianfedora.pro/koji/taskinfo?taskID=70427