There are many databases as this is a relatively large field of study.  You might already know about:  The European Bioinformatics Institute  concerning SARfari, the KinBase for regulatory kinases, and  the Human Kinome and Kinweb for human kinases, KinasPhos for the catalytic site, for example.  But if might be good to start with some information about the protein.  For example, is it involved in any particular pathway such as metabolism or transduction signalling?  Why is the protein suspected of having kinase activity?  You might try another approach called K-ISS:  Published June 22, 2015 // JCB vol. 209 no. 6 895-912

The Rockefeller University Press, doi: 10.1083/jcb.201412008

© 2015 Amano et al.,  Tools,  "Kinase-interacting substrate screening is a novel method to identify kinase substrates,"

Mutsuki Amano,1 Tomonari Hamaguchi,1 Md. Hasanuzzaman Shohag,1 Kei Kozawa,1 Katsuhiro Kato,1 Xinjian Zhang,1 Yoshimitsu Yura,1 Yoshiharu Matsuura,2 Chikako Kataoka,2 Tomoki Nishioka,1 and Kozo Kaibuchi1

I assume you are interested in protein regulatory proteins and are taking an experimental approach.  I have not done this but had been involved in one of the kinase programs in a company where LC/MS/MS technology is involved in discovering protein substrates with the putative kinase in an immobilized modality targeting a particular tissue and cell type.  It may be applicable to you since you already have the putative kinase isolated and, I assume, sequenced 

Thank you, Grant. The servers you recommended will come very handy as more direction is needed before getting the pipettes out for this project. May the 4th be with you!

Once past the bioinformatics stage, if you still feel your candidate protein is a protein kinase, you could try using a fairly non-specific substrate such as myelin basic protein as a starting point. Another approach would be to try to identify the 'pseudo substrate' sequenced in the putative kinase, if there is one, and then have a peptide synthesized that corresponds to this sequence but contains a phosphorylatable amino acid (S,T,Y). Of course, these approaches will require the use of [gamma32P]ATP and access to a lab with the appropriate equipment.

Many thanks for suggesting these elegant approaches, Bruce. May the 4th be with you too!