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It is good practice to rename a version-number-only tarball to something more speaking using the :: syntax, e.g.
source=("$pkgname-$pkgver.tar::https://github.com/$pkgname/$pkgname/archive/$pkgver.tar.gz")

Also you could provide docs, and as upstream no longer provides docs in texinfo format, replace texinfo makedpendeny with python-sphinx.

# Maintainer: youngunix

pkgname=flycheck
pkgver=31
pkgrel=1
pkgdesc='Modern on-the-fly syntax checking extension for GNU Emacs'
arch=('any')
url="http://www.flycheck.org/"
license=('GPL')
# groups=('emacs-plugins')
depends=('emacs' 'emacs-dash')
makedepends=('emacs' 'python-sphinx')
source=("$pkgname-$pkgver.tar.gz::https://github.com/flycheck/flycheck/archive/$pkgver.tar.gz")
sha256sums=('6c2447f6740afd394880f233641113d06f67f40fd696ee6f5034a84b2fcb9b3e')

build() {
cd "$pkgname-$pkgver"

emacs --batch -f batch-byte-compile flycheck.el
}

package() {
cd "$pkgname-$pkgver"

install -d "$pkgdir/usr/share/emacs/site-lisp/flycheck"
install -Dm644 flycheck.{el,elc} "$pkgdir/usr/share/emacs/site-lisp/flycheck"
cd doc
make BUILDDIR="$pkgdir"/usr/share/doc/$pkgname/ html
}

Suggesting an optional dependency for ruby (which provides checking for YAML and possibly others).

I wasnot refering to the build issues with my comment. If someone uses SRCDEST in makepkg.conf to point to a special directory for all sources, it may happen that there is a file 30.taz.gz from another project totally unrelated to flyspell. Therefore it is good practice to rename such short named files.

Version naming was not the issue.
Wouldn't build with 'skip' for sha256sums, generated one locally!
Other build errors fixed!

package builds successfully now.

It is good practice to rename a version-number-only tarball to something more speaking using the :: syntax, e.g.
source=("$pkgname-$pkgver.tar::https://github.com/flycheck/flycheck/archive/$pkgver.tar.gz")

==> Making package: flycheck 0.30-1 (Thu Feb 2 10:32:46 EET 2017)
==> Retrieving sources...
-> Found 30.tar.gz
==> Validating source files with sha256sums...
30.tar.gz ... FAILED
==> ERROR: One or more files did not pass the validity check!
:: failed to verify flycheck integrity

Installation fails due to the error above.

Thank you for pointing out the issue.
Download source issue fixed, try it now.

Source needs to be updated to http://stable.melpa.org/packages/flycheck-30.tar, package currently fails downloading source from github.

Tha install file can go away, as pacman hooks do this job now.

You are missing "seq" which is part of the "coreutils" package. Install it and try again. If you do get this error "flycheck.el:74:13:Error: Cannot open load file: no such file or directory, let-alist", I'm still working on which set includes "let-alist" (I'm assuming haskell).