You can give this a try. Serialize your objects to string using some method you have in place (JSON, XML, etc); then write the string to a ByteArray and compress it. The Base64 encode the compressed bytearray so you can pass it as text.
Other option could be using Flash native serializing format (AMF). This could be done too with a ByteArray, using the methods writeObject and readObject. (You should call registerClassAlias previously if you want to preserve the type information). Once you serialized your data to AMF, base64 encode the bytearray and pass it as text. Not sure if it makes sense to compress it; most likely not, since AMF is already compressed, but you could try both compressed and uncompressed and see if there's a significant difference.
Also, depending on your data, you could hand craft some kind of adhoc compression scheme that cannot be applied in the general case, but this will be more involved and will not neccesarily give the best results. I have a feeling that AMF will be a better option.